Chen, A, Li, X: Darboux transformation and soliton solutions for Boussinesq-Burgers equation. Chaos Solitons Fractals 27, 43-49 (2006)
Article
MathSciNet
MATH
Google Scholar
Jin-Ming, Z, Yao-Ming, Z: The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq-Burgers equation. Chin. Phys. B 20, Article ID 010205 (2011)
Article
Google Scholar
Kamchatnov, A, Kraenkel, A, Umarov, B: Asymptotic soliton train solutions of Kaup-Boussinesq equations. Wave Motion 38, 355-365 (2003)
Article
MathSciNet
MATH
Google Scholar
Mhlanga, I, Khalique, CM: Exact solutions of generalized Boussinesq-Burgers equations and \((2+1)\)-dimensional Davey-Stewartson equations. J. Appl. Math. 2012, Article ID 389017 (2012)
MathSciNet
MATH
Google Scholar
Khalique, CM: Exact solutions and conservation laws of a coupled integrable dispersionless system. Filomat 26, 957-964 (2012)
Article
MathSciNet
MATH
Google Scholar
Matveev, V, Salle, M: Darboux Transformation and Solitons. Springer, Berlin (1991)
Book
MATH
Google Scholar
Wang, Z, Chen, A: Explicit solutions of Boussinesq-Burgers equation. Chin. Phys. 16, 1233-1238 (2007)
Article
Google Scholar
Wazwaz, AM: Two integrable extensions of the Kadomtsev-Petviashvili equation. Cent. Eur. J. Phys. 91, 49-56 (2011)
Google Scholar
Wazwaz, AM: Solitons and singular solitons for a variety of Boussinesq-like equations. Ocean Eng. 53, 1-5 (2012)
Article
Google Scholar
Wazwaz, AM: Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers’ type equations. Commun. Nonlinear Sci. Numer. Simul. 14, 2962-2970 (2009)
Article
MathSciNet
MATH
Google Scholar
Wazwaz, AM: A study on the \((2+1)\)-dimensional and the \((2+1)\)-dimensional higher-order Burgers equations. Appl. Math. Lett. 25, 1495-1499 (2012)
Article
MathSciNet
MATH
Google Scholar
Wazwaz, AM: Combined equations of the Burgers hierarchy: multiple kink solutions and multiple singular kink solutions. Phys. Scr. 82, Article ID 025001 (2010)
Article
MATH
Google Scholar
Wazwaz, AM: Kinks and travelling wave solutions for Burgers-like equations. Appl. Math. Lett. 38, 174-179 (2014)
Article
MathSciNet
MATH
Google Scholar
Wazwaz, AM: Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities. Nonlinear Dyn. 83, 591-596 (2016)
Article
MathSciNet
MATH
Google Scholar
Wazwaz, AM: Multiple kink solutions for two coupled integrable \((2 + 1)\)-dimensional systems. Appl. Math. Lett. 58, 1-6 (2016)
Article
MathSciNet
MATH
Google Scholar
Hirota, R: Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27, 1192-1194 (1971)
Article
MATH
Google Scholar
Hirota, R: Exact N-soliton solutions of a nonlinear wave equation. J. Math. Phys. 14, 805-809 (1973)
Article
MathSciNet
MATH
Google Scholar
Jaradat, HM, Al-Shara’, S, Awawdeh, F, Alquran, M: Variable coefficient equations of the Kadomtsev-Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions. Phys. Scr. 85, Article ID 035001 (2012)
Article
MATH
Google Scholar
Jaradat, HM, Awawdeh, F, Al-Shara’, S, Alquran, M, Momani, S: Controllable dynamical behaviors and the analysis of fractal Burgers hierarchy with the full effects of inhomogeneities of media. Rom. J. Phys. 60(3-4), 324-343 (2015)
Google Scholar
Awawdeh, F, Jaradat, HM, Al-Shara’, S: Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma. Eur. Phys. J. D 66, 1-8 (2012)
Google Scholar
Awawdeh, F, Al-Shara’, S, Jaradat, HM, Alomari, AK, Alshorman, R: Symbolic computation on soliton solutions for variable coefficient quantum Zakharov-Kuznetsov equation in magnetized dense plasmas. Int. J. Nonlinear Sci. Numer. Simul. 15(1), 35-45 (2014)
Article
MathSciNet
Google Scholar
Wazwaz, AM: Multiple soliton solutions for the \((2+1)\)-dimensional asymmetric Nizhnik Novikov Veselov equation. Nonlinear Anal. 72, 1314-1318 (2010)
Article
MathSciNet
MATH
Google Scholar
Wazwaz, AM: Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192, 479-486 (2007)
MathSciNet
MATH
Google Scholar
Jaradat, HM: New solitary wave and multiple soliton solutions for the time-space fractional Boussinesq equation. Ital. J. Pure Appl. Math. 36, 367-376 (2016)
MathSciNet
MATH
Google Scholar
Alsayyed, O, Jaradat, HM, Jaradat, MMM, Mustafa, Z, Shatat, F: Multi-soliton solutions of the BBM equation arisen in shallow water. J. Nonlinear Sci. Appl. 9(4), 1807-1814 (2016)
MathSciNet
MATH
Google Scholar
Jaradat, HM: Dynamic behavior of traveling wave solutions for a class for the time-space coupled fractional kdV system with time-dependent coefficients. Ital. J. Pure Appl. Math. 36, 945-958 (2016)
MathSciNet
MATH
Google Scholar
Alquran, M, Jaradat, HM, Al-Shara’, S, Awawdeh, F: 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, 259-269 (2015)
MathSciNet
Google Scholar
Jaradat, HM: Dynamic behavior of traveling wave solutions for new couplings of the Burgers equations with time-dependent variable coefficients. Adv. Differ. Equ. 2017, Article ID 167 (2017). doi:10.1186/s13662-017-1223-1
Article
MathSciNet
Google Scholar
Jaradat, HM, Al-Shara’, S, Jaradat, MMM, Mustafa, Z, Alsayyed, O, Alquran, M, Abohassan, KM, Momani, S: New solitary wave and multiple soliton solutions for the time-space coupled fractional mKdV system with time-dependent coefficients. J. Comput. Theor. Nanosci. 13(12), 1-8 (2016)
Article
Google Scholar
Jaradat, HM, Syam, M, Alquran, M: Necessary conditions of coupled mkdV-BLMP system for multiple-soliton solutions to exist. Alex. Eng. J. (2017). doi:10.1016/j.aej.2017.06.012
Google Scholar
Zhang, ZY: New exact traveling wave solutions for the nonlinear Klein-Gordon equation. Turk. J. Phys. 32, 235-240 (2008)
Google Scholar
Zhang, ZY, Liu, ZH, Miao, XJ, Chen, YZ: New exact solutions to the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity. Appl. Math. Comput. 216, 3064-3072 (2010)
MathSciNet
MATH
Google Scholar
Zhang, ZY, Li, YX, Liu, ZH, Miao, XJ: New exact solutions to the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity via modified trigonometric function series method. Commun. Nonlinear Sci. Numer. Simul. 16(8), 3097-3106 (2011)
Article
MathSciNet
MATH
Google Scholar
Zhang, ZY, Zhang, YH, Gan, XY, Yu, DM: A note on exact traveling wave solutions for the Klein-Gordon-Zakharov equations. Z. Naturforsch. A 67(3-4), 167-172 (2014)
Google Scholar
Zhang, ZY, Liu, ZH, Miao, XJ, Chen, YZ: Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity. Phys. Lett. A 375, 1275-1280 (2011)
Article
MathSciNet
MATH
Google Scholar
Zhang, ZY, Gan, XY, Yu, DM: Bifurcation behavior of the traveling wave solutions of nonlinear the perturbed nonlinear Schrodinger equation with Kerr law nonlinearity. Z. Naturforsch. A 66(12), 721-727 (2014)
Google Scholar
Zhang, ZY, Zhong, J, Dou, S, Liu, J, Peng, D, Gao, T: A new method to construct traveling wave solutions for the Klein-Gordon-Zakharov equations. Rom. J. Phys. 58(7-8), 766-777 (2013)
Google Scholar
Zhang, ZY, Huang, J, Zhong, J, Dou, SS, Liu, J, Peng, D, Gao, T: The extended \((G'/G)\)-expansion method and travelling wave solutions for the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity. Pramana 82(6), 1011-1029 (2014)
Article
Google Scholar
Zhang, ZY, Zhong, J, Dou, SS, Liu, J, Peng, D, Gao, T: Abundant exact traveling wave solutions for the Klein-Gordon-Zakharov equations via the tanh-coth expansion method and Jacobi elliptic function expansion method. Rom. J. Phys. 58(7-8), 749-765 (2013)
Google Scholar
Zhang, ZY, Zhong, J, Dou, SS, Liu, J, Peng, D, Gao, T: First integral method and exact solutions to nonlinear partial differential equations arising in mathematical physics. Rom. Rep. Phys. 65(4), 1155-1169 (2013)
Google Scholar
Khater, AH, Callebaut, DK, Malfliet, W, Seadawy, AR: Nonlinear dispersive Rayleigh-Taylor instabilities in magnetohydrodynamic flows. Phys. Scr. 64, 533-547 (2001)
Article
MATH
Google Scholar
Khater, AH, Callebaut, DK, Seadawy, AR: Nonlinear dispersive instabilities in Kelvin-Helmholtz magnetohydrodynamic flows. Phys. Scr. 67, 340-349 (2003)
Article
MATH
Google Scholar
Khater, AH, Callebaut, DK, Seadawy, AR: General soliton solutions of an n-dimensional complex Ginzburg-Landau equation. Phys. Scr. 62, 353-357 (2000)
Article
MathSciNet
Google Scholar
Khater, AH, Callebaut, DK, Helal, MA, Seadawy, AR: Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line. Eur. Phys. J. D 39, 237-245 (2006)
Google Scholar
Khater, AH, Callebaut, DK, Seadawy, AR: General soliton solutions for nonlinear dispersive waves in convective type instabilities. Phys. Scr. 74, 384-393 (2006)
Article
MathSciNet
MATH
Google Scholar
Seadawy, AR: New exact solutions for the KdV equation with higher order nonlinearity by using the variational method. Comput. Math. Appl. 62, 3741-3755 (2011)
Article
MathSciNet
MATH
Google Scholar
Helal, MA, Seadawy, AR: Benjamin-Feir instability in nonlinear dispersive waves. Comput. Math. Appl. 64, 3557-3568 (2012)
Article
MathSciNet
MATH
Google Scholar
Seadawy, AR: Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas. Pramana J. Phys. 89(3), Article ID 49 (2017)
Article
Google Scholar
Seadawy, AR: Modulation instability analysis for the generalized derivative higher order nonlinear Schrodinger equation and its the bright and dark soliton solutions. J. Electromagn. Waves Appl. 31(14), 1353-1362 (2017)
Article
Google Scholar
Seadawy, AR: Traveling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves. Eur. Phys. J. Plus 132(29), 1-13 (2017)
Google Scholar
Wazwaz, AM: Multiple soliton solutions and other exact solutions for a two-mode KdV equation. Math. Methods Appl. Sci. 40, 2277-2283 (2017). doi:10.1002/mma.4138
Article
MathSciNet
MATH
Google Scholar
Wazwaz, AM: 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, 3977-3985 (2017). doi:10.1007/s40819-016-0302-4
Article
MathSciNet
Google Scholar
Wazwaz, AM: Two-mode fifth-order KdV equations: necessary conditions for multiple-soliton solutions to exist. Nonlinear Dyn. 87, 1685-1691 (2017). doi:10.1007/s11071-016-3144-z
Article
MathSciNet
Google Scholar
Korsunsky, SV: Soliton solutions for a second-order KdV equation. Phys. Lett. A 185, 174-176 (1994)
Article
MathSciNet
MATH
Google Scholar
Syam, M, Jaradat, H, Alquran, M: A study on the two-mode coupled modified Korteweg-de Vries using the simplified bilinear and the trigonometric-function methods. Nonlinear Dyn. 90(2), 1363-1371 (2017)
Article
MathSciNet
Google Scholar
Jaradat, HM, Syam, M, Alquran, M: A two-mode coupled Korteweg-de Vries: multiple-soliton solutions and other exact solutions. Nonlinear Dyn. 90(1), 371-377 (2017)
Article
MathSciNet
Google Scholar
Jaradat, HM: Two-mode coupled Burgers equation: multiple-kink solutions and other exact solutions. Alex. Eng. J. (2017). doi:10.1016/j.aej.2017.06.014
Google Scholar
Hirota, R: Exact solution of the modified Korteweg-de Vries equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33, 1456-1458 (1972)
Article
Google Scholar
Shukri, S, Al-Khaled, K: The extended tanh method for solving systems of nonlinear wave equations. Appl. Math. Comput. 217(5), 1997-2006 (2010)
MathSciNet
MATH
Google Scholar
Qawasmeh, A, Alquran, M: Reliable study of some new fifth-order nonlinear equations by means of \((G^{\prime}/G)\)-expansion method and rational sine-cosine method. Appl. Math. Sci. 8(120), 5985-5994 (2014)
Google Scholar
Qawasmeh, A, Alquran, M: Soliton and periodic solutions for \((2+1)\)-dimensional dispersive long water-wave system. Appl. Math. Sci. 8(50), 2455-2463 (2014)
MathSciNet
Google Scholar
Alquran, M, Al-Khaled, K: The tanh and sine-cosine methods for higher order equations of Korteweg-de Vries type. Phys. Scr. 84, Article ID 025010 (2011)
Article
MATH
Google Scholar
Alquran, M, Al-Khaled, K: Sinc and solitary wave solutions to the generalized Benjamin-Bona-Mahony-Burgers equations. Phys. Scr. 83, Article ID 065010 (2011)
Article
MATH
Google Scholar