Many kinds of travelling wave solutions of the KdV-Burgers-Kuramoto equation including the solitary wave solutions are presented by applying the trial function approach. The results obtained are in agreement with those given in existing reference.

KdV-Burgers-Kuramoto equation, trial function approach, travelling wave solution, solitary wave solution

Received: December 30, 2024; Accepted: January 30, 2025; Published: January 30, 2025

How to cite this article: Yuan-Xi Xie, Solutions to the KdV-Burgers-Kuramoto equation, Far East Journal of Applied Mathematics 118(1) (2025), 1-10. http://dx.doi.org/10.17654/0972096025001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Amer. J. Phys. 60 (1992), 650-654.
[2] E. G. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000), 212-218.
[3] S. K. Liu, Z. T. Fu and S. D. Liu, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A 289 (2001), 69-74.
[4] E. J. Parkes, B. R. Duffy and P. C. Abbott, The Jacobi elliptic function method for finding periodic-wave solutions to nonlinear evolution equations, Phys. Lett. A 295 (2002), 280-286.
[5] Y. X. Xie and J. S. Tang, A unified trial function method in finding the explicit and exact solutions to three NPDEs, Phys. Scr. 74 (2006), 197-200.
[6] Y. X. Xie, Explicit and exact solutions to the KdV-Burgers equation, Nuovo Cimento B 121 (2006), 689-697.
[7] Y. X. Xie, Explicit and exact solutions to the mKdV-sine-Gordon equation, Mod. Phys. Lett. B 22 (2008), 1471-1485.
[8] Y. X. Xie, A combination method and its applications to nonlinear evolution equations, Int. J. Mod. Phys. B 26 (2012), 1250110-1-1250110-10.
[9] Y. X. Xie, Seeking the explicit exact solutions of sinh-Poisson type equations by a modified auxiliary ODE technique, Far East J. Appl. Math. 87(2) (2014), 159-180.
[10] Z. T. Fu, S. D. Liu and S. K. Liu, Notes on solutions to Burgers-type equations, Commun. Theor. Phys. (Beijing) 41 (2004), 527-530.
[11] Z. T. Fu, S. K. Liu and S. D. Liu, New exact solutions to the KdV-Burgers-Kuramoto equation, Chaos Solitons Fractals 23 (2005), 609-616.