On extracting new wave solutions to a modified nonlinear Schrödinger’s equation using two integration methods

Liu, 2020, Deep learning for Feynman’s path integral in strong-field time-dependent dynamics, Phys Rev Lett, 124, 10.1103/PhysRevLett.124.113202 Yang, 2021, Wave mixing and high-harmonic generation enhancement by a two-color field driven dielectric metasurface, Chin Opt Lett, 19, 10.3788/COL202119.123202 Lu, 2021, Rotational nonlinear double-beam energy harvesting, Smart Mater Struct, 31, 10.1088/1361-665X/ac4579 Djilali, 2020, Turing-hopf bifurcation in a diffusive mussel-algae model with time-fractional-order derivative, Chaos Solitons Fractals, 138, 10.1016/j.chaos.2020.109954 Shen, 2022, Microstructure understanding of high Cr-Ni austenitic steel corrosion in high-temperature steam, Acta Mater, 10.1016/j.actamat.2022.117634 Roshani, 2016, Flow regime independent volume fraction estimation in three-phase flows using dual-energy broad beam technique and artificial neural network, Neural Comput Appl, 28, 1265, 10.1007/s00521-016-2784-8 Zhao, 2019, On approximating the quasi-arithmetic mean, J Inequal Appl, 2019, 42, 10.1186/s13660-019-1991-0 Ghanbari, 2020, Mathematical analysis of a fractional-order predator– prey model with prey social behavior and infection developed in predator population, Chaos Solitons Fractals, 138, 10.1016/j.chaos.2020.109960 Zhao, 2021, Monotonicity and convexity involving generalized elliptic integral of the first kind, Rev Real Acad Cienc Exact Fis Nat A, 115, 46 Ghanbari, 2020, An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator–prey model, Chaos Solitons Fractals, 138, 10.1016/j.chaos.2020.109910 Liu, 2022, Understanding the stress corrosion cracking growth mechanism of a cold worked alumina-forming austenitic steel in supercritical carbon dioxide, Corros Sci, 199, 10.1016/j.corsci.2022.110179 Ghanbari, 2019, A novel technique to construct exact solutions for nonlinear partial differential equations, Eur Phys J Plus, 134, 10.1140/epjp/i2019-13037-9 Ju, 2022, On the preferential grain boundary oxidation of a Ni-Co-based superalloy, Corros Sci, 199, 10.1016/j.corsci.2022.110203 Chu, 2015, Convexity and concavity of the complete elliptic integrals with respect to lehmer mean, J Inequal Appl, 2015, 396, 10.1186/s13660-015-0926-7 Rashid, 2022, Some further extensions considering discrete proportional fractional operators, Fractals, 30, 10.1142/S0218348X22400266 Nazeer, 2022, Theoretical study of mhd electro-osmotically flow of third-grade fluid in micro channel, Appl Math Comput, 420 Zhao, 2021, Sharp bounds for the weighted hölder mean of the zero-balanced generalized complete elliptic integrals, Comput Methods Funct Theory, 21, 413, 10.1007/s40315-020-00352-7 Roshani, 2021, Proposing a gamma radiation based intelligent system for simultaneous analyzing and detecting type and amount of petroleum by-products, Nucl Eng Technol, 53, 1277, 10.1016/j.net.2020.09.015 Zhao, 2020, Convexity and concavity of the modified bessel functions of the first kind with respect to hölder means, Rev Real Acad Cienc Exact Fís Natl A, 114, 1 Ghanbari, 2019, Numerical solution of predator–prey model with beddington-deangelis functional response and fractional derivatives with Mittag-Leffler kernel, Chaos, 29, 10.1063/1.5094546 Chu, 2020, Sharp bounds for the toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means, Math Slovaca, 70, 1097, 10.1515/ms-2017-0417 Guo, 2022, Understanding the fretting corrosion mechanism of zirconium alloy exposed to high temperature high pressure water, Corros Sci, 10.1016/j.corsci.2022.110300 Roshani, 2018, Density and velocity determination for single-phase flow based on radiotracer technique and neural networks, Flow Meas Instrum, 61, 9, 10.1016/j.flowmeasinst.2018.03.006 Zhao, 2021, Concavity and bounds involving generalized elliptic integral of the first kind, J Math Inequal, 15, 701, 10.7153/jmi-2021-15-50 Zhang, 2022, Advanced point-of-care testing technologies for human acute respiratory virus detection, Adv Mater, 34, 10.1002/adma.202103646 Zhao, 2020, A sharp double inequality involving generalized complete elliptic integral of the first kind, AIMS Math, 5, 4512, 10.3934/math.2020290 Guo, 2022, Understanding the fretting corrosion mechanism of zirconium alloy exposed to high temperature high pressure water, Corros Sci, 10.1016/j.corsci.2022.110300 Singh, 2022, Analysis of fractional model of guava for biological pest control with memory effect, J Adv Res, 32, 99, 10.1016/j.jare.2020.12.004 Karami, 2018, Enhancing the performance of a dual-energy gamma ray based three-phase flow meter with the help of grey wolf optimization algorithm, Flow Meas Instrum, 64, 164, 10.1016/j.flowmeasinst.2018.10.015 Zhao, 2013, Best possible bounds for neuman-sándor mean by the identric, quadratic and contraharmonic means, Abstr Appl Anal, 2013 Zhao, 2022, Landen inequalities for gaussian hypergeometric function, Racsam Rev R Acad A, 116, 53 Zhao, 2021, On approximating the arc lemniscate functions, Indian J Pure Appl Math Ghanbari, 2020, Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels, Adv Differ Equ, 2020, 435, 10.1186/s13662-020-02890-9 Zhao, 2018, Quadratic transformation inequalities for Gaussian hypergeometric function, J Inequal Appl, 2018, 251, 10.1186/s13660-018-1848-y Sattari, 2021, Applicability of time-domain feature extraction methods and artificial intelligence in two-phase flow meters based on gamma-ray absorption technique, Measurement, 168 Djilali, 2021, Dynamical behavior of two predators-one prey model with generalized functional response and time-fractional derivative, Adv Differ Equ, 2021, 235, 10.1186/s13662-021-03395-9 Djilali, 2021, The influence of an infectious disease on a preypredator model equipped with a fractional-order derivative, Adv Differ Equ, 2021, 20, 10.1186/s13662-020-03177-9 Ghanbari, 2021, Chaotic behaviors of the prevalence of an infectious disease in a prey and predator system using fractional derivatives, Math Methods Appl Sci, 44, 9998, 10.1002/mma.7386 Roshani, 2017, Intelligent recognition of gas-oil-water threephase flow regime and determination of volume fraction using radial basis function, Flow Meas Instrum, 54, 39, 10.1016/j.flowmeasinst.2016.10.001 Iqbal, 2022, Study on date–jimbo–kashiwara– miwa equation with conformable derivative dependent on time parameter to find the exact dynamic wave solutions, Fract Fract, 6, 4, 10.3390/fractalfract6010004 Zhao, 2015, Monotonicity properties of a function involving the psi function with applications, J Inequal Appl, 2015, 193, 10.1186/s13660-015-0724-2 Akinyemi, 2021, New optical solitons of perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion, Results Phys, 29, 10.1016/j.rinp.2021.104656 Nisar, 2022, New perturbed conformable Boussinesq-like equation: Soliton and other solutions, Results Phys, 10.1016/j.rinp.2022.105200 Nisar, 2022, New solutions for the generalized resonant nonlinear Schrödinger equation, Results Phys, 10.1016/j.rinp.2021.105153 Yépez-Martínez, 2022, The novel soliton solutions for the conformable perturbed nonlinear Schrödinger equation, Modern Phys Lett B, 36, 10.1142/S0217984921505977 Yao, 2021, Dynamics of optical solitons in higher-order Sasa–Satsuma equation, Results Phys, 30, 10.1016/j.rinp.2021.104825 Akinyemi, 2022, Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index, Nonlinear Anal: Model Control, 27, 1, 10.15388/namc.2022.27.26374 Jia, 2021, Breather, soliton and rogue wave of a two-component derivative nonlinear Schrödinger equation, Phys Lett A, 405, 10.1016/j.physleta.2021.127426 Wazwaz, 2019, Optical solitons and Peregrine solitons for nonlinear Schrödinger equation by variational iteration method, Optik, 179, 804, 10.1016/j.ijleo.2018.11.004 Wazwaz, 2019, Optical solitons and Peregrine solitons for nonlinear Schrödinger equation by variational iteration method, Optik, 179, 804, 10.1016/j.ijleo.2018.11.004 Wazwaz, 2018, A new nonlinear integrable fifth-order equation: multiple soliton solutions with unusual phase shifts, Phys Scr, 93, 10.1088/1402-4896/aaded5 Kaur, 2019, Bright–dark optical solitons for Schrödinger-Hirota equation with variable coefficients, Optik, 179, 479, 10.1016/j.ijleo.2018.09.035 Ghanbari, 2018, A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation, Eur Phys J Plus, 133, 142, 10.1140/epjp/i2018-11984-1 Hajiseyedazizi, 2021, On multi-step methods for singular fractional q-integro-differential equations, Open Math, 19, 1378, 10.1515/math-2021-0093 Song, 2015, Optimal evaluation of a toader-type mean by power mean, J Inequal Appl, 2015, 408, 10.1186/s13660-015-0927-6 Roshani, 2018, Online measuring density of oil products in annular regime of gas-liquid two phase flows, Measurement, 129, 296, 10.1016/j.measurement.2018.07.026 Nabti, 2021, Global stability analysis of a fractional SVEIR epidemic model, Math Methods Appl Sci, 44, 8577, 10.1002/mma.7285 Wang, 2020, Inequalities for generalized trigonometric and hyperbolic functions with one parameter, J Math Inequal, 14, 1, 10.7153/jmi-2020-14-01 Ghanbari, 2020, On approximate solutions for a fractional prey-predator model involving the Atangana-Baleanu derivative, Adv Differ Equ, 2020, 679, 10.1186/s13662-020-03140-8 Ghanbari, 2020, A fractional system of delay differential equation with nonsin- gular kernels in modeling hand-foot-mouth disease, Adv Differ Equ, 2020, 536, 10.1186/s13662-020-02993-3 Zhao, 2012, Optimal bounds for neuman-sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic means, Abstr Appl Anal, 2012, 10.1155/2012/302635 Karami, 2018, Investigation of different sources in order to optimize the nuclear metering system of gas-oil-water annular flows, Neural Comput Appl, 32, 3619, 10.1007/s00521-018-3673-0 Chu, 2014, Optimal bounds for neuman-sándor mean in terms of the convex combination of logarithmic and quadratic or contra-harmonic means, J Math Inequal, 8, 201, 10.7153/jmi-08-13 Wang, 2022, Pore structure heterogeneity of wufeng-longmaxi shale, Sichuan Basin, China: Evidence from gas physisorption and multifractal geometries, J Pet Sci Eng, 208, 10.1016/j.petrol.2021.109313 Ghanbari, 2020, Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method, Adv Differ Equ, 2020, 328, 10.1186/s13662-020-02787-7 Xu, 2022, Sharp bounds for the lemniscatic mean by the one-parameter geometric and quadratic means, Rev Real Acad Cienc Exact Fís Natl A, 116, 1 Ghanbari, 2019, The new exact solitary wave solutions and stability analysis for the (2+1)-dimensional Zakharov-Kuznetsov equation, Adv Differ Equ, 2019, 49, 10.1186/s13662-019-1964-0 Roshani, 2020, Application of GMDH neural network technique to improve measuring precision of a simplified photon attenuation based two-phase flowmeter, Flow Meas Instrum, 75, 10.1016/j.flowmeasinst.2020.101804 Zhao, 2021, Sharp power mean bounds for the lemniscate type means, Rev Real Acad Cienc Exact Fís Natl A, 115, 1 Srivastava, 2019, Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the kerr law nonlinearity, Math Methods Appl Sci, 42, 7210, 10.1002/mma.5827 Ghanbari, 2021, A new model for investigating the transmission of infectious diseases in a prey-predator system using a non-singular fractional derivative, Math Methods Appl Sci, 10.1002/mma.7386 Roshani, 2017, Intelligent densitometry of petroleum products in stratified regime of two phase flows using gamma ray and neural network, Flow Meas Instrum, 58, 6, 10.1016/j.flowmeasinst.2017.09.007 Rahman, 2020, On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals, Adv Differ Equ, 368 Chu, 2016, Concavity of the error function with respect to Hölder means, Math Inequal Appl, 19, 589 Roshani, 2015, Flow regime identification and void fraction prediction in two-phase flows based on gamma ray attenuation, Measurement, 62, 25, 10.1016/j.measurement.2014.11.006 Karthikeyan, 2021, Almost sectorial operators on ψ-Hilfer derivative fractional impulsive integrodifferential equations, Math Methods Appl Sci, 10.1002/mma.7954 Ghanbari, 2020, A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative, Chaos Solitons Fractals, 133, 10.1016/j.chaos.2020.109619 Wang, 2022, Renewable quantile regression for streaming datasets, Knowl Based Syst, 235, 10.1016/j.knosys.2021.107675 Huang, 2022, Simultaneous realization of polarization conversion for reflected and transmitted waves with bi-functional metasurface, Sci Rep, 12 Meng, 2018, H∞ Optimal performance design of an unstable plant under bode integral constraint, Complexity, 2018, 10.1155/2018/4942906 Zhang, 2021, ROSEFusion: random optimization for online dense reconstruction under fast camera motion, ACM Trans Graph, 40, 1, 10.1145/3450626.3459783 Zhao, 2022, Learning practically feasible policies for online 3D bin packing, Sci China Inf Sci, 65, 1, 10.1007/s11432-021-3348-6 Jin, 2022, On nonlinear evolution model for drinking behavior under Caputo–fabrizio derivative, J Appl Anal Comput He, 2022, Fractional-order discretetime SIR epidemic model with vaccination: Chaos and complexity, Mathematics, 10, 165, 10.3390/math10020165 Wang, 2022, Numerical solution of traveling waves in chemical kinetics: Time fractional Fishers equations, Fractals, 30, 10.1142/S0218348X22400515 Roshani, 2021, Combination of x-ray tube and GMDH neural network as a nondestructive and potential technique for measuring characteristics of gas-oil-water three phase flows, Measurement, 168, 10.1016/j.measurement.2020.108427 Chu, 2021, Enhancement in thermal energy and solute particles using hybrid nanoparticles by engaging activation energy and chemical reaction over a parabolic surface via finite element approach, Fract Fract, 5, 119, 10.3390/fractalfract5030119 Chu, 2014, Sharp bounds for Neuman-Sándor mean in terms of the convex combination of quadratic and first seiffert means, Acta Math Sci, 34, 797, 10.1016/S0252-9602(14)60050-3 Roshani, 2017, Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Prog Nucl Energy, 98, 29, 10.1016/j.pnucene.2017.02.004 Nazemi, 2016, Optimization of a method for identifying the flow regime and measuring void fraction in a broad beam gamma-ray attenuation technique, Int J Hydrog Energy, 41, 7438, 10.1016/j.ijhydene.2015.12.098 Zha, 2022, On the bounds of the perimeter of an ellipse, Acta Math Sci, 42, 491, 10.1007/s10473-022-0204-y Nazemi, 2016, Precise void fraction measurement in two-phase flows independent of the flow regime using gamma-ray attenuation, Nucl Eng Technol, 48, 64, 10.1016/j.net.2015.09.005 Roshani, 2017, Usage of two transmitted detectors with optimized orientation in order to three phase flow metering, Measurement, 100, 122, 10.1016/j.measurement.2016.12.055 Rashid, 2022, Some recent developments on dynamical ħ-discrete fractional type inequalities in the frame of nonsingular and nonlocal kernels, Fractals, 30, 10.1142/S0218348X22401107 Adineh-Vand, 2014, Precise volume fraction prediction in oil-water-gas multiphase flows by means of gamma-ray attenuation and artificial neural networks using one detector, Measurement, 51, 34, 10.1016/j.measurement.2014.01.030 Zhao, 2021, Sharp power mean bounds for the tangent and hyperbolic sine means, J Math Inequal, 15, 1459, 10.7153/jmi-2021-15-100 Ghanbari, 2019, An analytical method for soliton solutions of perturbed Schrödinger’s equation with quadratic-cubic nonlinearity, Modern Phys Lett B, 33, 10.1142/S0217984919500180 Roshani, 2016, Investigation of using 60 co source and one detector for determining the flow regime and void fraction in gas-liquid two-phase flows, Flow Meas Instrum, 50, 73, 10.1016/j.flowmeasinst.2016.06.013 Zhang, 2022, Transcranial focused ultrasound stimulation of periaqueductal gray for analgesia, IEEE Trans Biomed Eng, 10.1109/TBME.2022.3162073 Munusamy, 2020, Existence of solutions for some functional integrodifferential equations with nonlocal conditions, Math Methods Appl, 43, 10319, 10.1002/mma.6698 Roshani, 2021, Evaluation of flow pattern recognition and void fraction measurement in two phase flow independent of oil pipeline’s scale layer thickness, Alex Eng J, 60, 1955, 10.1016/j.aej.2020.11.043 Ghanbari, 2019, New solitary wave solutions and stability analysis of the Benney-Luke and the Phi-4 equations in mathematical physics, Aims Math, 4, 1523, 10.3934/math.2019.6.1523 Chu, 2014, Sharp bounds for the neuman mean in terms of the quadratic and second seiffert means, J Inequal Appl, 2014, 299, 10.1186/1029-242X-2014-299 Sun, 2014, A note on the Neuman-Sándor mean, J Math Inequal, 8, 287, 10.7153/jmi-08-20 Ghanbari, 2020, A constructive method for solving the equation Xa=b in Rn: A generalization of division in Rn, Appl Math, 364 Wang, 2021, A review of wind speed and wind power forecasting with deep neural networks, Appl Energy, 304, 10.1016/j.apenergy.2021.117766 Zhao, 2020, On some refinements for inequalities involving zero-balanced hypergeometric function, AIMS Math, 5, 6479, 10.3934/math.2020418 Gao, 2019, Dispersing mechanism and tribological performance of vegetable oil-based CNT nanofluids with different surfactants, Tribol Int, 131, 51, 10.1016/j.triboint.2018.10.025 Guo, 2017, Experimental evaluation of the lubrication performance of mixtures of castor oil with other vegetable oils in MQL grinding of nickel-based alloy, J Clean Prod, 140, 1060, 10.1016/j.jclepro.2016.10.073 Zhou, 2021, Overview of underwater transmission characteristics of oceanic LiDAR, IEEE J Sel Top Appl Earth Obs Remote Sens, 14, 8144, 10.1109/JSTARS.2021.3100395 Zhang, 2018, Experimental assessment of an environmentally friendly grinding process using nanofluid minimum quantity lubrication with cryogenic air, J Clean Prod, 193, 236, 10.1016/j.jclepro.2018.05.009 Li, 2016, Grinding temperature and energy ratio coefficient in MQL grinding of high-temperature nickel-base alloy by using different vegetable oils as base oil, Chin J Aeronaut, 29, 1084, 10.1016/j.cja.2015.10.012 Zhou, 2021, An innovative echo detection system with STM32 gated and PMT adjustable gain for airborne LiDAR, Int J Remote Sens, 42, 9187, 10.1080/01431161.2021.1975844 Ghanbari, 2021, On the modeling of an eco-epidemiological model using a new fractional operator, Results Phys, 21, 10.1016/j.rinp.2020.103799 Zhou, 2021, Gaussian inflection point selection for LiDAR hidden echo signal decomposition, IEEE Geosci Remote Sens Lett, 19, 1 Qiao, 2022, Fastest-growing source prediction of US electricity production based on a novel hybrid model using wavelet transform, Int J Energy Res, 46, 1766, 10.1002/er.7293 Qiao, 2021, An innovative coupled model in view of wavelet transform for predicting short-term PM10 concentration, J Environ Manage, 289, 10.1016/j.jenvman.2021.112438 Zhang, 2022, Hydrate deposition model and flow assurance technology in gas-dominant pipeline transportation systems: A review, Energy Fuels, 36, 1747, 10.1021/acs.energyfuels.1c03812 Biswas, 2007 Zhang, 2010, New exact solutions to the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity, Appl Math Comput, 216, 3064 Kohl, 2008, Optical soliton perturbation in a non-Kerr law media, Opt Laser Technol, 40, 647, 10.1016/j.optlastec.2007.10.002 Green, 2010, Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media, Commun Nonlinear Sci Numer Simul, 15, 3865, 10.1016/j.cnsns.2010.01.018 Osman, 2018, New optical solitary wave solutions of fokas-lenells equation in presence of perturbation terms by a novel approach, Optik, 175, 328, 10.1016/j.ijleo.2018.08.007 Ghanbari, 2021, On the nondifferentiable exact solutions to schamel’s equation with local fractional derivative on Cantor sets, Numer Methods Partial Differ Equ Ghanbari, 2021, Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative, Math Methods Appl Sci, 44, 8759, 10.1002/mma.7302 Ghanbari, 2019, Solitary wave solutions to the Tzitzeica type equations obtained by a new efficient approach, Appl Anal Comput, 9, 568 Ghanbari, 2021, On novel nondifferentiable exact solutions to local fractional Gardner’s equation using an effective technique, Math Methods Appl Sci, 44, 4673, 10.1002/mma.7060 Ghanbari, 2021, New analytical solutions for the Oskolkov-type equations in fluid dynamics via a modified methodology, Results Phys, 28, 10.1016/j.rinp.2021.104610 Aldhabani, 2022, Abundant solitary wave solutions to a perturbed Schrödinger equation with Kerr law nonlinearity via a novel approach, Results Phys, 35, 10.1016/j.rinp.2022.105385 Zha, 2021, A fuzzy-based strategy to suppress the novel coronavirus (2019-ncov) massive outbreak, Appl Comput Math, 20, 160 Ghanbari, 2021, On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators, Chaos Solitons Fractals, 150, 10.1016/j.chaos.2021.111136 Chu, 2022, Combined impact of cattaneo-christov double diffusion and radiative heat flux on bio-convective flow of maxwell liquid configured by a stretched nano-material surface, Appl Math Comput, 419 Yang, 2019, Predictive model for minimum chip thickness and size effect in single diamond grain grinding of zirconia ceramics under different lubricating conditions, Ceram Int, 45, 14908, 10.1016/j.ceramint.2019.04.226 Ghanbari, 2021, Employing Hirota’s bilinear form to find novel lump waves solutions to an important nonlinear model in fluid mechanics, Results Phys, 29, 10.1016/j.rinp.2021.104689 Ghanbari, 2021, Mathematical and numerical analysis of a three-species predator–prey model with herd behavior and time fractional-order derivative, Math Methods Appl Sci, 43, 1736, 10.1002/mma.5999 Zhao, 2021, Artificial neural networking (ann) analysis for heat and entropy generation in flow of non-newtonian fluid between two rotating disks, Math Methods Appl Sci, 10.1002/mma.7310 Zhang, 2015, Experimental research on the energy ratio coefficient and specific grinding energy in nanoparticle jet MQL grinding, Int J Adv Manuf Syst, 78, 1275, 10.1007/s00170-014-6722-6 Ghanbari, 2020, On the modeling of the interaction between tumor growth and the immune system using some new fractional and fractional-fractal operators, Adv Differ Equ, 2020, 585, 10.1186/s13662-020-03040-x