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

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.

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Cited by in corpus (1)

• Multi-soliton solutions and data-driven discovery of higher-order Burgers' hierarchy equations with physics informed neural networks