Data-driven wave solutions of (2+1)-dimensional nonlinear dispersive long wave equation by deep learning

Abstract

In this paper, we introduce a deep learning framework to solve the (2+1)-dimensional nonlinear dispersive long wave equation. Using it, we study the data-driven solitary wave solutions, periodic wave solutions, kink wave solutions and various multiple soliton solutions for the equations with initial–boundary value conditions. On the one hand, we obtain the data-driven traveling wave solutions of the equations, which have high accuracy compared with corresponding exact traveling wave solutions. On the other hand, we set more complicated initial–boundary value problems of the equations, whose exact traveling wave solution cannot be easy to obtain, but our network still works well and gives its numerical solution. The results show that our deep learning algorithm is able to accurately capture the dynamical behavior of traveling waves of the (2+1)-dimensional nonlinear dispersive long wave equation.