A deep learning method for solving high-order nonlinear soliton equation

TL;DR

This paper introduces a deep learning approach to solve high-order nonlinear soliton equations, demonstrating its effectiveness on complex equations like the Boussinesq and KdV equations, and revealing soliton interactions.

Contribution

It presents a novel deep learning scheme tailored for high-order nonlinear soliton equations, including comparison of activation functions and validation on significant equations.

Findings

Deep learning effectively solves high-order nonlinear soliton equations.

The method accurately captures soliton interactions.

Activation function choice impacts solution accuracy.

Abstract

We propose effective scheme of deep learning method for high-order nonlinear soliton equation and compare the activation function for high-order soliton equation. The neural network approximates the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equation, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg de Vries equation. The results show that deep learning method can solve the high-order nonlinear soliton equation and reveal the interaction between solitons.