References
[1] M.J. Ablowitz and P.A. Clarkson, Soliton, Nonlinear Evolution Equations and Inverse Scattering, Cambridge Univ. Press, New York, 1991. CrossRef

[2] I. Aslan, Multi-wave and rational solutions for nonlinear evolution equations, Int. J. Nonlinear Sci. Numer. Simul. 11 (2010), 619–623. CrossRef

[3] I. Aslan, Rational and multi-wave solutions to some nonlinear physical models, Rom. J. Phys. 58 (2013), 893–903.

[4] C.Q. Dai, Y. Fan, and N. Zhang, Re-observation on localized waves constructed by variable separation solutions of (1+1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method, Appl. Math. Lett. 96 (2019), 20–26. CrossRef

[5] U.C. De and K. Mandal, Ricci solitons and gradient Ricci solitons on N(k)paracontact manifolds, Zh. Mat. Fiz. Anal. Geom. 15 (2019), 369–378. CrossRef

[6] E.G. Fan, Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation, Phys. Lett. A 282 (2001), 18–22. CrossRef

[7] C.S. Gardner, J.M. Greene, M.D. Kruskal, and R.M. Miura, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett. 19 (1967), 1095–1097. CrossRef

[8] J.H. He and M.A. Abdou, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos Soliton. Fract. 34 (2007), 1421–1429. CrossRef

[9] J.H. He, F.Y. Ji, and H. Mohammad-Sedighi, Difference equation vs differential equation on different scales, Internat. J. Numer. Methods Heat Fluid Flow 31 (2021), 391-401 CrossRef

[10] J.H. He and X.H. Wu, Exp-function method for nonlinear wave equations, Chaos Soliton. Fract. 30 (2006), 700–708. CrossRef

[11] R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192–1194. CrossRef

[12] F.Y. Ji, C.H. He, J.J. Zhang, and J.H. He,A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar, Appl. Math. Model. 32 (2020), 437–448. CrossRef

[13] Z.Z. Kang and T.C. Xia, Multi-solitons for the coupled Fokas–Lenells system via Riemann–Hilbert approach, Chinese Phys. Lett. 35 (2018), Article ID 070201. CrossRef

[14] C.Z. Li and H.J. Zhou, Solutions of the Frobenius coupled KP equation, Zh. Mat. Fiz. Anal. Geom. 15 (2019), 369–378. CrossRef

[15] Y. Liu, Y.T. Gao, Z.Y. Sun, and X. Yu, Multi-soliton solutions of the forced variablecoefficient extended Korteweg-de Vries equation arisen in fluid dynamics of internal solitary waves, Nonlinear Dyn. 66 (2011), 575–587. CrossRef

[16] W.H. Liu and Y.F. Zhang, Multiple rogue wave solutions for a (3+1)-dimensional Hirota bilinear equation, Appl. Math. Lett. 98 (2019), 184–190. CrossRef

[17] A. Maccari, The Kadomtsev-Petviashvili equation as a source of integrable model equations, J. Math. Phys. 37 (1996), 6207–6212. CrossRef

[18] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Amer. J. Phys. 60 (1992), 650–654. CrossRef

[19] W.J. Rui and Y.F. Zhang, Soliton and lump-soliton solutions in the Grammian form for the Bogoyavlenskii–Kadomtsev–Petviashvili equation, Adv. Differential Equations 2020 (2020), Article ID 195. CrossRef

[20] V.N. Serkin, A. Hasegawa, and T.L. Belyaeva, Nonautonomous solitons in external potentials, Phys. Rev. Lett. 98 (2007), Article ID 074102. CrossRef

[21] X.Y. Shan and J.Y. Zhu, The Mikhauilov–Novikov–Wang hierarchy and its Hamiltonian structures, Acta Phys. Pol. B 43 (2012), 1953–1963. CrossRef

[22] D.D. Shi and Y.F. Zhang, Diversity of exact solutions to the conformable space-time fractional MEW equation, Appl. Math. Lett. 99 (2020), Article ID 105994. CrossRef

[23] B. Xu and S. Zhang, A novel approach to time-dependent-coefficient WBK system: doubly periodic waves and singular nonlinear dynamics, Complexity, 2018 (2018), Article ID 3158126. CrossRef

[24] B. Xu and S. Zhang, Integrability, exact solutions and nonlinear dynamics of a nonisospectral integral-differential system, Open Phys. 17 (2019), 299–306. CrossRef

[25] B. Xu and S. Zhang, Exact solutions with arbitrary functions of the (4+1)dimensional Fokas equation, Therm. Sci. 23 (2019), No. 4, 2403–2411. CrossRef

[26] B. Xu and S. Zhang, Derivation and soliton dynamics of a new non-isospectral and variable-coefficient system, Therm. Sci. 23 (2019), Suppl. 3, S639–S646. CrossRef

[27] B. Xu, L.J. Zhang, and S. Zhang, Analytical insights into three models: exact solutions and nonlinear vibrations, J. Low Freq. Noise Vib. Active Control 38 (2019), 901–913. CrossRef

[28] Z.Y. Yan and H.Q. Zhang, New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water, Phys. Lett. A 285 (2001), 355–362. CrossRef

[29] S. Zhang, Exp-function method for constructing explicit and exact solutions of a lattice equation, Appl. Math. Comput. 199 (2008), 242–249. CrossRef

[30] S. Zhang and M.A. Abdou, Exact solutions of the mKdV and Sawada-Kotera equations with variable coefficients via exp-function method, J. Appl. Math. Inform. 28 (2010), 143–152.

[31] S. Zhang and B. Cai, Multi-soliton solutions of a variable-coefficient KdV hierarchy, Nonlinear Dyn. 78 (2014), 1593–1600. CrossRef

[32] S. Zhang, J.H. Li, and L.Y Zhang, A direct algorithm of exp-function method for non-linear evolution equations in fluids, Therm. Sci. 20 (2016), 881–884. CrossRef

[33] S. Zhang and T.C. Xia, A generalized F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equations, Appl. Math. Comput. 183 (2006), 1190– 1200. CrossRef

[34] S. Zhang and T.C. Xia, A generalized auxiliary equation method and its application to (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations, J. Phys. A: Math. Theor. 40 (2007), 227–248. CrossRef

[35] S. Zhang and T.C. Xia, A further improved tanh function method exactly solving the (2+1)-dimensional dispersive long wave equations, Appl. Math. E-Notes 8(2008), 58–66.

[36] S. Zhang, B. Xu, and H.Q. Zhang, Exact solutions of a KdV equation hierarchy with variable coefficients, Int. J. Comput. Math. 91 (2014), 1601–1616. CrossRef

[37] S. Zhang, C.H. You, and B. Xu, Simplest exp-function method for exact solutions of Mikhauilov-Novikov-Wang equations, Therm. Sci. 23 (2019), 2381–2388. CrossRef

[38] S. Zhang and H.Q. Zhang, Discrete Jacobi elliptic function expansion method for nonlinear differential-difference equations, Phys. Scripta, 80 (2009) Article ID 045002. CrossRef

[39] S. Zhang and H.Q. Zhang, Exp-function method for N-soliton solutions of nonlinear differential-difference equations, Z. Naturforsch. A 65 (2010), 924–934. CrossRef

[40] S. Zhang and H.Q. Zhang, A transformed rational function method for (3+1)dimensional potential YTSF equation, Pramana J. Phys. 76 (2011), 561–571. CrossRef

[41] S. Zhang, L.J. Zhang, and B. Xu, Rational waves and complex dynamics: analytical insights into a generalized nonlinear Schrödinger equation with distributed coefficients, Complexity 2019 (2019), Article ID 3206503. CrossRef

[42] S. Zhang and Q.A. Zong,Exact solutions with external linear functions for the potential Yu-Toda–Sasa–Fukuyama equation, Therm. Sci. A 22 (2018), 1621–1628. CrossRef

[43] Y.B. Zhou, M.L. Wang, and Y.M. Wang, Periodic wave solutions to a coupled KdV equation with variable coefficients, Phys. Lett. A 308 (2003), 31–36. CrossRef