[1]

Ablowitz M.J., Clarkson P.A., Solitons, 1990, Cambridge University Press, Cambridge Google Scholar

[2]

Vakhnenko V.O., Parkes E.J., Morrison A.J., A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Soliton Fract., 2003, 17, 683–692. CrossrefGoogle Scholar

[3]

Hirota R., Backlund Transformations, Springer, Berlin, 1980 Google Scholar

[4]

Lu D., Hong B., Tian L., New explicit exact solutions for the generalized coupled Hirota–Satsuma KdV system, Comput. Math. Appl., 2007, 53, 1181–1190. Web of ScienceCrossrefGoogle Scholar

[5]

Bian C., Pang J., Jin L., Ying X., Solving two fifth order strong nonlinear evolution equations by using the *G*^{′}/*G*-expansion method, Commun. Nonlinear Sci. Numer. Simul., 2010, 15, 2337–2343.Web of ScienceCrossrefGoogle Scholar

[6]

Kudryashov N.A., A note on the *G*^{′}/*G*-expansion method, Appl. Math. Comput., 2010, 217(4), 1755–1758.Web of ScienceGoogle Scholar

[7]

Olver P.J., Applications of Symmetry Methods to Partial Differential Equations, Springer-Verlag, New-York, 1986 Google Scholar

[8]

Cimpoiasu R., Constantinescu R., Cimpoiasu V.M., Integrability of dynamical systems with polynomial Hamiltonians, Rom. J. Phys., 2005, 50(3-4), 317–324. Google Scholar

[9]

Cimpoiasu R., Constantinescu R., Lie Symmetries for Hamiltonian Systems Methodological Approach, Int. J.Theor. Phys., 2006, 45(9), 1769–1782. CrossrefGoogle Scholar

[10]

Xu M.J., Tian S.F., Tu J.M., Zhang T.T., Lie symmetry analysis, conservation laws, solitary and periodic waves for a coupled Burger equation, Superlattice Microst., 2017, 101, 415-428. Web of ScienceCrossrefGoogle Scholar

[11]

Tu J.M., Tian S.F., Xu M.J., Zhang T.T., On Lie symmetries, optimal systems and explicit solutions to the Kudryashov–Sinelshchikov equation, Appl. Math. Comput., 2016, 275, 345-352. Web of ScienceGoogle Scholar

[12]

Bhrawy A.H., Abdelkawy M.A., Kumar S., Biswas A., Solitons and other solutions to Kadomtsev-Petviashvili equation of B-type, Rom. J. Phys., 2013, 58, 729–748. Google Scholar

[13]

Biswas A., Solitary waves for power-law regularized long-wave equation and R (m, n) equation, Nonlinear Dyn., 2010, 59, 423–426. Web of ScienceCrossrefGoogle Scholar

[14]

Cimpoiasu R., Generalized conditional symmetries and related solutions of the Grad-Shafranov equation, Phys. Plasmas, 2014, 21(4), 042118-1–042118-7. Web of ScienceGoogle Scholar

[15]

Su K., Cao J., Third-Order Conditional Lie–Bäcklund Symmetries of Nonlinear Reaction-Diffusion, Adv. Math. Phys., 2017, 2017, 2825416-1–2825416-9. Google Scholar

[16]

Tian S.F., Zhang H.Q., On the Integrability of a Generalized Variable-Coefficient Forced Korteweg-de Vries Equation in Fluids, Stud. Appl. Math., 2014, 132(3), 212-246. CrossrefWeb of ScienceGoogle Scholar

[17]

Wang X.B., Tian S.F., Qin C.Y., Zhang T.T., Characteristics of the breathers, rogue waves and solitary waves in a generalized (2+1)-dimensional Boussinesq equation, Europhys. Lett., 2016, 115, 10002-1-10002-5. Web of ScienceGoogle Scholar

[18]

Wang X.B., Tian S.F., Xu M.J., Zhang T.T., On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation, Appl. Math. Comput., 2016, 283, 216-233. Web of ScienceGoogle Scholar

[19]

Tian S.F., Initial-boundary value problems for the general coupled nonlinear Schrodinger equation on the interval via the Fokas method, J. Differ. Equations, 2017, 262, 506-558. Web of ScienceCrossrefGoogle Scholar

[20]

Benny D.J., A general theory for interactions between short and long waves, Stud. Appl. Math., 1977, 56(1), 81–94. CrossrefGoogle Scholar

[21]

Djordjevic V.D., Redekopp L.G., On two-dimensional packets of capillary-gravity waves, J. Fluid Mech., 1977, 79(4), 703–714. CrossrefGoogle Scholar

[22]

Xin J., Guo B., Han Y., Huang D., The global solution of the (2+ 1)-dimensional long wave–short wave resonance interaction equation, J. Math. Phys., 2008, 49(7), 073504-1-073504-13. Web of ScienceGoogle Scholar

[23]

Guo B.L., Wang B.X., The global solution and its long time behavior for a class of generalized LS type equations, Prog Nat. Sci., 1996, 6(5), 533–546. Google Scholar

[24]

Ma Y.C., The Complete Solution of the Long-Wave–Short-Wave Resonance Equations, Stud. Appl. Math., 1978, 59(3), 201–221. CrossrefGoogle Scholar

[25]

Laurencot P.H., On a nonlinear Schrödinger equation arising in the theory of water waves, Nonlinear Anal.-Theor., 1995, 24(4), 509–523. CrossrefGoogle Scholar

[26]

Guo B., Chen I., Orbital stability of solitary waves of the long–short resonance equations, Math. Meth. Appl. Sci., 1998, 21, 883–894. CrossrefGoogle Scholar

[27]

Feng Z.S., The first-integral method to study the Burgers–Korteweg–de Vries equation, J. Phys. A-Math. Gen., 2002, 35, 343–349. CrossrefGoogle Scholar

[28]

Jafari H., Soltani R., Khalique C.M., Baleanu D., On the exact solutions of nonlinear long-short wave resonance equations, Rom. Rep. Phys., 2015, 67(3), 762–772. Google Scholar

[29]

Shang Y., The extended hyperbolic function method and exact solutions of the long–short wave resonance equations, Chaos Soliton Fract., 2008, 36(3), 762–772. CrossrefWeb of ScienceGoogle Scholar

[30]

Cimpoiasu R., Travelling wave solutions for the long-short wave resonance model by an improved *G*^{′}/*G*-expansion method, Rom. J. Phys., 2018, (accepted paper), http://www.nipne.ro/rjp/accpaps/016-Cimpoi_3A41FA.pdf

[31]

Gurefe Y., Misirli E., Sonmezoglu A., Ekici M., Extended trial equation method to generalized nonlinear partial differential equations, App. Math. Comput., 2013, 219(10), 5253–5260. CrossrefGoogle Scholar

[32]

Zayed E.M., Moatimid G.M., Al-Nowehy A.G., The generalized Kudryashov method and its applications for solving nonlinear PDEs in mathematical physics, Sci. J. Math. Res., 2015, 5, 19–39. Google Scholar

[33]

Liu C.S., Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations, Comput. Phys. Commun., 2010, 181(2),
317–324. CrossrefWeb of ScienceGoogle Scholar

[34]

Kudryashov N.A., One method forfinding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul., 2012, 17, 2248–2253. CrossrefGoogle Scholar

[35]

Shang Y., Huang Y., Yuan W., The extended hyperbolic functions method and new exact solutions to the Zakharov equations, Appl. Math. Comput., 2008, 200(1), 110–122. Web of ScienceGoogle Scholar

[36]

Zuo J.M., Application of the extended *G*^{′}/*G*-expansion method to solve the Pochhammer–Chree equations, Appl. Math. Comput., 2010, 217(1), 376–383. Web of ScienceGoogle Scholar

[37]

Bridges T.J., Multi-symplectic structures and wave propagation, Math. Proc. Camb. Phil. Soc., 1997, 121, 147-190. CrossrefGoogle Scholar

[38]

Hu W., Deng Z., Zhang Y., Multi-symplectic method for peakon-antipeakon collision of quasi-Degasperis-Procesi equation, Comput. Phys. Commun., 2014, 185, 2020-2028. Web of ScienceCrossrefGoogle Scholar

[39]

Hu W., Deng Z., Yin T., Almost structure-preserving analysis for weakly linear damping nonlinear Schrodinger equation with periodic perturbation, Commun Nonlinear Sci. Numer Simulat., 2017, 42, 298–312. CrossrefGoogle Scholar

[40]

Hu W., Deng Z., Competition between geometric dispersion and viscous dissipation in wave propagation of KdV-Burgers equation, J. Vib. Control, 2015, 21, 2937-2945. Web of ScienceCrossrefGoogle Scholar

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