Some new soliton solutions and dynamical behaviours of (3+1)-dimensional Jimbo-Miwa equation

Abstract

Some new solitary solutions of (3+1)-dimensional Jimbo-Miwa equation such as breather solutions, double breather solutions and mixed solutions of different forms are studied via applying Hirota's bilinear form and constructing various trial functions. Besides, the degradation phenomenon of breather solution to lump-type solution is investigated, and dynamical behaviours of the interaction between solitary solutions and lump-type solutions varying with time t is discussed. Finally, the interactive result between N-soliton solution (N takes any positive integer) and lump-type solution is studied by reducing dimension, and the detailed proof process is presented.

Keywords:

• Hirota's bilinear form
• Jimbo-Miwa equation
• evolution behaviour of solitons
• breather solution

2020 Mathematics Subject Classifications:

• 35C08
• 35Q51

Acknowledgments

It is gratefully acknowledged that this research was supported by the National Natural Science Foundation of P.R. China [grant number 51974377], and the Natural Science Foundation of Hunan Province, China [grant numbers 2021JJ30548 and 2021JJ40434]. Furthermore, We are grateful to the reviewers for their valuable comments and suggestions.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51974377], and the Natural Science Foundation of Hunan Province, China [grant numbers 2021JJ30548, 2021JJ40434].