On the breathers and rogue waves to a (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients

ABSTRACT

In this paper, we construct new breather wave and rogue wave solutions for the (2+1)-dimensional nonlinear Schrödinger equation (NLS) with variable coefficients by using similarity transformations. The similarity transformation helps us to relate certain class of rogue wave and breather wave solutions of the (2+1)-dimensional NLS equation to the solutions of integrable NLS equation with variable coefficients. Moreover, the new rational solutions to the equation with potentials and nonlinearities depending on both spatial and time coordinates are considered. Finally, the dynamics of the new rational solutions is graphically discussed. It is interesting that the new rational solutions can describe interactions of line rogue waves (or breather wave) and periodic line waves.

Keywords:

• A (2+1)-dimensional nonlinear Schrödinger ((2+1)-DNLS) equation with variable coefficients
• rogue wave
• breather wave

Acknowledgments

We express our sincere thanks to the Editor and the Referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Key Research and Development Program of China [grant number 2017YFB0202901] and the National Natural Science Foundation of China [grant number 11871180].