Some new dynamical behaviour of double breathers and lump-N-solitons for the Ito equation

Abstract

Based on symbolic computation and Hirota bilinear method, we investigate the evolution and degeneration behaviour of breather-wave solution with different forms for the Ito equation. Some new lump solutions are obtained in the process of studying the degeneration of breather-wave solution. Besides, the spatio-temporal evolution of the interaction phenomenon of lump-N-soliton $(N\to \mathrm{\infty })$ is studied. An existence theorem about the lump-N-soliton is given and proved. The lump-N-soliton of different combinations is studied to show the correctness and effectiveness of the given theorem and corollary, such as lump-cos type, lump-double breathers type and lump-N-soliton type. To better show the evolutionary behaviour of lump-N-soliton with the change of soliton number N and time t, we give some three-dimensional structure figure with projections. Finally, some novel non-linear dynamical behaviours, including the degeneration of breathers, the emergence of lump solutions, the fission and fusion of lump-N-soliton, the superposition of lump-N-soliton and so on, analysed and simulated.

Keywords:

• Ito equation
• lump-N-soliton
• double breather-waves
• fusion and fission of solitons
• superposition behaviour

2010 Mathematics Subject Classifications:

• 35Q51
• 35Q53
• 35C08

Acknowledgments

It is gratefully acknowledged that this research was supported by the National Natural Science Foundation of P.R. China. We are grateful to the reviewers for their encouraging suggestions that were helpful in improving this paper further.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the National Natural Science Foundation of P.R. China [grant number 11661037].