Nonlinear Dynamics

, Volume 87, Issue 4, pp 2635–2642

# Lump solution and integrability for the associated Hirota bilinear equation

Original Paper

## Abstract

This paper studies lump solution and integrability for the associated Hirota bilinear equation. The integrability in the sense of Lax pair and the bilinear Bäcklund transformations is presented by the binary Bell polynomial method. The lump solution is derived when the period of complexiton solution goes to infinite. Conversely, complexiton solution can also be derived from the lump solution. Complexiton solution is a superposition structure of lump solutions. The dynamics of the lump solution are investigated and exhibited mathematically and graphically. These results further supplement and enrich the theories for the associated Hirota bilinear equation. It is hoped that these results might provide us with useful information on the dynamics of the relevant fields in nonlinear science.

## Keywords

Binary Bell polynomial Hirota’s bilinear form Bäcklund transformation Lax pair Complexiton solution Lump solution

## Notes

### Acknowledgements

The author would like to express his sincere thanks to referees for their enthusiastic guidance and help. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11501266, 11661047) and the Fund for Fostering Talents in Kunming University of Science and Technology (No: KKSY201403049).

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