Shapes and dynamics of dual-mode Hirota–Satsuma coupled KdV equations: Exact traveling wave solutions and analysis

Guo, 2013, Dynamic behaviors of the breather solutions for the AB system in fluid mechanics, Nonlinear Dyn., 74, 701, 10.1007/s11071-013-0998-1

Guo, 2014, Breathers and localized solitons for the Hirota-Maxwell-Bloch system on constant backgrounds in erbium doped fibers, Ann. Phys., 344, 10, 10.1016/j.aop.2014.02.006

Yang, 2018, Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation, Appl. Math. Lett., 82, 64, 10.1016/j.aml.2018.02.018

Li, 2018, Generation mechanism of rogue waves for the discrete nonlinear Schrödinger equation, Appl. Math. Lett., 83, 110, 10.1016/j.aml.2018.03.018

Li, 2016, Rational solitons in the parity-time-symmetric nonlocal nonlinear Schrödinger model, J. Phys. Soc. Jpn., 85, 124001, 10.7566/JPSJ.85.124001

Zhang, 2017, Dark soliton solutions of the defocusing Hirota equation by the binary Darboux transformation, Nonlinear Dyn., 89, 531, 10.1007/s11071-017-3469-2

Zhang, 2017, Darboux transformation and dark soliton solution for the defocusing sasa-satsuma equation, Appl. Math. Lett., 69, 101, 10.1016/j.aml.2017.02.012

Zhang, 2017, Binary Darboux transformation for the coupled Sasa-Satsuma equations, Chaos, 27, 073102, 10.1063/1.4986807

Zhang, 2017, General n-dark vector soliton solution for multi-component defocusing Hirota system in optical fiber media, Commun. Nonlinear Sci. Numer. Simul., 51, 124, 10.1016/j.cnsns.2017.03.019

Korsunsky, 1994, Soliton solutions for a second-order KdV equation, Phys. Lett. A, 185, 174, 10.1016/0375-9601(94)90842-7

Lee, 2007

Hirota, 1981, Soliton solutions of a coupled Korteweg-de Vries equation, Phys. Lett. A, 85, 407, 10.1016/0375-9601(81)90423-0

Wazwaz, 2017, Multiple soliton solutions and other exact solutions for a two-mode KdV equation, Math. Methods Appl. Sci., 40, 1277, 10.1002/mma.4138

Xiao, 2016, Multi-soliton solutions and Bucklund transformation for a two-mode KdV equation in a fluid, Waves Random Complex Media, 31, 1

Lee, 2011, A hamiltonian model and soliton phenomenon for a two-mode KdV equation, Rocky Mount. J. Math., 41, 1273, 10.1216/RMJ-2011-41-4-1273

Lee, 2010, Quasi-solitons of the two-mode Korteweg-de Vries equation, Eur. Phys. J. Appl. Phys., 52, 11301, 10.1051/epjap/2010132

Lee, 2013, On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system, Waves Random Complex Media, 23, 56, 10.1080/17455030.2013.770585

Hong, 1999, New non-traveling solitary wave solutions for a second-order Korteweg-de Vries equation, Z. Naturforsch., 54a, 375, 10.1515/zna-1999-6-705

Alquran, 2017, Jacobi elliptic function solutions for a two-mode KdV equation, J. King Saud Univ., 10.1016/j.jksus.2017.06.010

Jaradat, 2018, Two-mode coupled burgers equation: multiple-kink solutions and other exact solutions, Alexandria Eng. J., 57, 2151, 10.1016/j.aej.2017.06.014

Syam, 2017, A study on the two-mode coupled modified Korteweg-de Vries using the simplified bilinear and the trigonometric-function methods, Nonlinear Dyn., 90, 1363, 10.1007/s11071-017-3732-6

Jaradat, 2017, A two-mode coupled Korteweg-de Vries: multiple-soliton solutions and other exact solutions, Nonlinear Dyn., 90, 371, 10.1007/s11071-017-3668-x

Alquran, 2018, A modified approach for a reliable study of new nonlinear equation: two-mode Korteweg-de Vries-Burgers equation, Nonlinear Dyn., 91, 1619, 10.1007/s11071-017-3968-1

Wazwaz, 2017, A two-mode burgers equation of weak shock waves in a fluid: multiple kink solutions and other exact solutions, Int. J. Appl. Comput. Math, 3, 3977, 10.1007/s40819-016-0302-4

Wazwaz, 2018, Two-mode Sharma-Tasso-Olver equation and two-mode fourth-order burgers equation: multiple kink solutions, Alexandria Eng. J., 57, 1971, 10.1016/j.aej.2017.04.003

Jaradat, 2018, A numerical study on weak-dissipative two-mode perturbed Burgers and Ostrovsky models: right-left moving waves, Eur. Phys. J. Plus., 133

Jaradat, 2018, Dark and singular optical solutions with dual-mode nonlinear Schrödinger’s equation and kerr-law nonlinearity, Optik, 172, 822, 10.1016/j.ijleo.2018.07.069

Alquran, 2018, Dynamism of two-mode’s parameters on the field function for third-order dispersive fisher: application for fibre optics, Opt. Quant. Electron., 50, 354, 10.1007/s11082-018-1621-y

Irwaq, 2018, New dual-mode Kadomtsev–Petviashvili model with strong-weak surface tension: analysis and application, Adv. Differ. Equ., 2018

Ismail, 2014, A numerical solution for Hirota–Satsuma coupled KdV equation, Abstract Appl. Anal., 819367

Qawasmeh, 2014, Reliable study of some new fifth-order nonlinear equations by means of g′/g expansion method and rational sine–cosine method, Applied Mathematical Sciences, 8, 5985, 10.12988/ams.2014.48669

Wang, 2018, A coupled KdV system: consistent tanh expansion, soliton-cnoidal wave solutions and nonlocal symmetries, Chin. J. Phys., 56, 598, 10.1016/j.cjph.2018.02.009

Arshad, 2018, Optical soliton perturbation for Gerdjikov-Ivanov equation via two analytical techniques, Chin. J. Phys., 56, 2879, 10.1016/j.cjph.2018.09.023

Kumar, 2018, Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chin. J. Phys., 56, 75, 10.1016/j.cjph.2017.11.020

Kudryashov, 2012, One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul., 17, 2248, 10.1016/j.cnsns.2011.10.016

Wang, 2018, Construction of new exact solutions to time-fractional two-component evolutionary system of order 2 via different methods, Opt. Quant. Electron., 50