By introducing a transformation and using an auxiliary function, many explicit and exact solutions for the nonlinear Poisson equation, which include the rational function solution, the solitary wave solutions, the singular traveling wave solutions and the trigonometric function periodic wave solutions, are successfully presented in a concise way.

auxiliary function, nonlinear Poisson equation, explicit and exact solutions

Received: February 25, 2021; Accepted: March 10, 2021; Published: June 15, 2021

How to cite this article: Yuan-Xi Xie, Explicit and exact solutions for the nonlinear Poisson equation, Far East Journal of Applied Mathematics 110(1)(2021), 19-26. DOI: 10.17654/AM110010019

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

References

[1] W. Malfliet, Amer. J. Phys. 60 (1992), 650.
[2] E. G. Fan, Phys. Lett. A 277 (2000), 212.
[3] M. L. Wang, Phys. Lett. A 199 (1995), 169.
[4] M. L. Wang, Y. B. Zhou and Z. B. Li, Phys. Lett. A 216 (1996), 67.
[5] S. K. Liu, Z. T. Fu and S. D. Liu, Phys. Lett. A 289 (2001), 69.
[6] E. J. Parkes, B. R. Duffy and P. C. Abbott, Phys. Lett. A 295 (2002), 280.
[7] Y. X. Xie, Chin. Phys. B 18 (2009), 5123.
[8] K. L. Su and Y. X. Xie, Int. J. Mod. Phys. B 25 (2011), 1101.
[9] Y. X. Xie, Nuovo Cimento B 123 (2008), 1607.
[10] Y. X. Xie, Int. J. Mod. Phys. B 26 (2012), 1250110-1.