A new two-mode coupled Burgers equation: Conditions for multiple kink solution and singular kink solution to exist

Korsunsky, 1994, Soliton solutions for a second-order KdV equation, Phys Lett, A185, 174, 10.1016/0375-9601(94)90842-7 Wazwaz, 2016, Multiple soliton solutions and other exact solutions for a two mode KdV equation, Math Methods Appl Sci Wazwaz, 2016, A two-mode burgers equation of weak shock waves in a fluid: multiple kink solutions and other exact solutions, Int J Appl Comput Math Wazwaz, 2017, Two-mode ffth-order KdV equations: necessary conditions for multiple-soliton solutions to exist, Nonlinear Dyn, 87, 1685, 10.1007/s11071-016-3144-z Hirota, 1971, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys Rev Lett, 27, 1192, 10.1103/PhysRevLett.27.1192 Hirota, 1972, Exact solution of the modified Korteweg-de Vries equation for multiple collisions of solitons, J Phys Soc Japan, 33 Wazwaz, 2009, Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers type equations, Commun Nonlinear Sci Numer Simul, 14, 2962, 10.1016/j.cnsns.2008.12.018 Wazwaz, 2014, Kinks and travelling wave solutions for Burgers-like equations, Appl Math Lett, 38, 174, 10.1016/j.aml.2014.08.003 Wazwaz, 2016, Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearity, Nonlinear Dynam, 83, 591, 10.1007/s11071-015-2349-x Hirota, 1973, Exact N-soliton solutions of a nonlinear wave equation, J Math Phys, 14, 805, 10.1063/1.1666399 Jaradat, 2012, Variable coefficient equations of the Kadomtsev-Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions, Phys Scr, 85, 10.1088/0031-8949/85/03/035001 Jaradat, 2015, Controllable dynamical behaviors and the analysis of fractal burgers hierarchy with the full effects of inhomogeneities of media, Roman J Phys, 60, 324 Awawdeh, 2012, Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma, Eur Phys J D, 66, 1, 10.1140/epjd/e2011-20518-0 Awawdeh, 2014, Symbolic computation on soliton solutions for variable coefficient quantum Zakharov-Kuznetsov equation in magnetized dense plasmas, Int J Nonlinear Sci Numer Simul, 15, 35, 10.1515/ijnsns-2012-0154 Wazwaz, 2007, Multiple-soliton solutions for the Boussinesq equation, Appl Math Comput, 192, 479, 10.1016/j.amc.2007.03.023 Jaradat, 2016, New solitary wave and multiple soliton solutions for the time-space fractional boussinesq equation, Italian J Pure Appl Math, 36, 367 Alsayyed, 2016, Multi-soliton solutions of the BBM equation arisen in shallow water, J Nonlinear Sci Appl, 9, 1807, 10.22436/jnsa.009.04.35 Jaradat, 2016, Dynamic behavior of traveling wave solutions for a class for the time-space coupled fractional kdV system with time-dependent coefficients, Italian J Pure Appl Math, 36, 945 Alquran, 2015, A new simplified bilinear method for the N-soliton solutions for a generalized FmKdV equation with time-dependent variable coefficients, Int J Nonlinear Sci Numer Simul, 16, 259, 10.1515/ijnsns-2014-0023 Jaradat, 2016, New solitary wave and multiple soliton solutions for the time-space coupled fractional mKdV system with time-dependent coefficients, J Comput Theoret Nanosci, 13, 9082, 10.1166/jctn.2016.6284 Jaradat, 2017, Dynamic behavior of traveling wave solutions for new couplings of the Burgers equations with time-dependent variable coefficients, advances in difference equations, Adv Diff Eqs, 2017, 167, 10.1186/s13662-017-1223-1 Tamsi, 2016, An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers equation, Appl Math Comput, 290, 111, 10.1016/j.amc.2016.05.048 Shukla, 2016, Modified cubic B-spline differential quadrature method for numerical solution of three dimensional coupled viscous Burger equation, Mod Phys Lett B, 30, 1650110, 10.1142/S0217984916501104 Tamsira, 2016, Extended modified cubic B-spline algorithm for nonlinear Burgers equation, Beni-suef Univ J Basic Appl Sci, 5, 244, 10.1016/j.bjbas.2016.09.001 Shukla, 2014, Numerical solution of two dimensional coupled viscous Burgers equation using the modified cubic B spline differential quadrature method, AIP Adv, 4, 117134, 10.1063/1.4902507 Srivastava, 2014, One-dimensional coupled Burgers equation and its numerical solution by an implicit logarithmic finite difference method, AIP Adv, 4, 037119, 10.1063/1.4869637 Srivastava, 2013, An implicit finite-difference solution to one dimensional coupled Burgers equations, Asian Eur J Math, 6, 10.1142/S1793557113500587 Srivastava, 2013, Generating exact solution of three dimensional coupled unsteady nonlinear generalized viscous Burgers equations, Int J Modern Math Sci, 5, 1 Ma, 2002, Complexiton solutions to the Korteweg-de Vires equation, Phys Lett A, 301, 35, 10.1016/S0375-9601(02)00971-4 Syam, 1999, Numerical differentiation of implicitly defined curves, J Comput Appl Math, 108, 131, 10.1016/S0377-0427(99)00106-5 Ma, 1997, Explicit exact solution of a generalized KdV equation, Acta Math Scripta, 17, 168 Ma, 2004, Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions, Trans Am Math Soc, 357, 1753, 10.1090/S0002-9947-04-03726-2 Ma, 2004, Rational solutions of the Toda lattice equation in Casoratian form, Chaos, Solit Fract, 22, 395, 10.1016/j.chaos.2004.02.011 Sabatti M, Fabbrini F, Harfouche A, Beritognolo I, Mareschi C, Carlini M, et al. Evolution of biomass production potential and heating value of hybrid poplar genotypes in a short-rotation culture in Italy. Indus Crops Prod 2014;61: 62–73 [ISNN 0926-8690]. El-Sayed, 2007, Electrohydrodynamic instability of a dielectric compressible liquid sheet streaming into an ambient stationary compressible gas, Arch Appl Mech, 77, 613, 10.1007/s00419-007-0118-0 Syam, 2007, The modified Broyden-variational method for solving nonlinear elliptic differential equations, Chaos Solit Fract, 32, 392, 10.1016/j.chaos.2005.04.126 Mohyud-Din, 2011, Numerical soliton solution of the Kaup-Kupershmidt equation, Int J Numer Methods Heat Fluid Flow, Emerald, 21, 272, 10.1108/09615531111108459 Mohyud-Din, 2011, Numerical soliton solutions of the improved Boussinesq equation, Int J Numer Meth Heat Fluid Flow, 21, 822, 10.1108/09615531111162800 Syam, 2005, Numerical solution of singularly perturbed fifth order two point boundary value problem, Appl Math Comput, 170, 1085, 10.1016/j.amc.2005.01.003 Attilia, 2006, An efficient implicit Runge-Kutta method for second order systems, Appl Math Comput, 178, 229, 10.1016/j.amc.2005.11.044 Alam, 2014, A novel -expansion method and its application to the Boussinesq equation, Chin Phys B, 23, 020203, 10.1088/1674-1056/23/2/020203 Mohyud-Din, 2009, Traveling wave solutions of seventh-order generalized KdV equations using Heís polynomials, Int J Nonlinear Sci Numer Simul, 10, 223, 10.1515/IJNSNS.2009.10.2.227 Syam M. Analytical solution of the fractional Fredholm integro-differential equation using the modified residual power series method. Complexity, 2017; 2017. p. 6. Noor, 2010, Exp-function method for traveling wave solutions of nonlinear evolution equations, Appl Math Comput, Elsevier, 216, 477, 10.1016/j.amc.2010.01.042 Mohyud-Din S, Noor M, Noor K. Some relatively new techniques for nonlinear problems. Math Prob Eng, Hindawi, 2009; 2009. p. 25. https://doi.org/10.1155/2009/234849 [Article ID 234849]. Noor, 2008, Exp-function method for generalized traveling solutions of master partial differential equations, Acta Appl Math, Springer, 104, 131, 10.1007/s10440-008-9245-z Mohyud-Din, 2010, Exp-function method for generalized traveling solutions of Calogero-Degasperis-Fokas equation, Zeitschrift fur Naturforschung A – A J Phys Sci, 65a, 78, 10.1515/zna-2010-1-208 Jiwari, 2015, A hybrid numerical scheme for the numerical solution of the Burgers equation, Comput Phys Commun, 188, 59, 10.1016/j.cpc.2014.11.004 Jiwari, 2013, A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers equation, Appl Math Comput, 219, 6680, 10.1016/j.amc.2012.12.035 Mittal, 2013, A numerical scheme based on differential quadrature method to solve time dependent Burgers equation, Eng Comput, 30, 117, 10.1108/02644401311286071 Kumar, 2014, A composite scheme for the numerical simulation of coupled Burgers equation, Comput Phys Commun, 185, 809, 10.1016/j.cpc.2013.11.012