Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation

Authors

Peijun Zhang
Weipeng Hu
Zhen Wang
Zhijun Qiao, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-5-2023

Abstract

Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the motion laws of the microparticles. As a local nonlinear dynamic behavior, the soliton-collision is difficult to be reproduced numerically. In this paper, the soliton-collision process in the nonlinear perturbed Schrödinger equation is simulated employing the multi-symplectic method. The multi-symplectic formulations are derived including the multi-symplectic form and three local conservation laws of the nonlinear perturbed Schrödinger equation. Employing the implicit midpoint rule, we construct a multi-symplectic scheme, which is equivalent to the Preissmann box scheme, for the nonlinear perturbed Schrödinger equation. The elegant structure-preserving properties of the multi-symplectic scheme are illustrated by the tiny maximum absolute residual of the discrete multi-symplectic structure at each time step in the numerical simulations. The effects of the perturbation strength on the soliton-collision in the nonlinear perturbed Schrödinger equation are reported in the numerical results in detail.

Comments

Copyright © 2023, The Author(s)

Recommended Citation

Zhang, Peijun, Weipeng Hu, Zhen Wang, and Zhijun Qiao. "Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation." Journal of Nonlinear Mathematical Physics 30, no. 4 (2023): 1467-1482. https://doi.org/10.1007/s44198-023-00137-1

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Journal of Nonlinear Mathematical Physics

DOI

https://doi.org/10.1007/s44198-023-00137-1