Lump and interaction solutions for a generalized (3 + 1)-dimensional propagation model of nonlinear waves in fluid dynamics

Abstract

In this paper, we focus on the lump and interaction solutions for a generalized (3 + 1)-dimensional propagation model of nonlinear waves in fluid dynamics. With symbolic computation, some new exact solutions which include lump, lump-periodic, lump-kink and lump-soliton solutions are presented by using the Hirota's bilinear method and test function method. The lump and interaction solutions are illustrated by three-dimensional plots and contour plots.

Keywords:

• A (3 + 1)-dimensional propagation model
• Hirota's bilinear method
• test function
• lump solution
• interaction solution

2010 Mathematics Subject Classifications:

• 35Q51
• 35Q53
• 74J30

Acknowledgments

The authors wish to thank the Editors and the Referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11461022], and the Natural Science Foundation of Yunnan Province, China, [grant number 2014FA037].