Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning

01/12/2021
by   Li Wang, et al.
9

In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves with discontinuous first-order derivative at the wave peak. In this paper, we apply the multi-layer physics-informed neural networks (PINNs) deep learning to successfully study the data-driven peakon and periodic peakon solutions of some well-known nonlinear dispersion equations with initial-boundary value conditions such as the Camassa-Holm (CH) equation, Degasperis-Procesi equation, modified CH equation with cubic nonlinearity, Novikov equation with cubic nonlinearity, mCH-Novikov equation, b-family equation with quartic nonlinearity, generalized modified CH equation with quintic nonlinearity, and etc. These results will be useful to further study the peakon solutions and corresponding experimental design of nonlinear dispersive equations.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 5

page 7

page 8

page 11

page 12

page 13

page 15

page 17

12/18/2020

Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning

The physics-informed neural networks (PINNs) can be used to deep learn t...
02/18/2021

Deep learning as closure for irreversible processes: A data-driven generalized Langevin equation

The ultimate goal of physics is finding a unique equation capable of des...
02/03/2021

Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation

We present a numerical study of solutions to the 2d focusing nonlinear S...
04/22/2020

Deflation-based Identification of Nonlinear Excitations of the 3D Gross–Pitaevskii equation

We present previously unknown solutions to the 3D Gross-Pitaevskii equat...
06/25/2021

On the continuum limit for the discrete Nonlinear Schrödinger equation on a large finite cubic lattice

In this study, we consider the nonlinear Schödinger equation (NLS) with ...
05/02/2022

Instabilities Appearing in Effective Field theories: When and How?

Nonlinear partial differential equations appear in many domains of physi...
09/01/2021

Physics-informed Neural Network for Nonlinear Dynamics in Fiber Optics

A physics-informed neural network (PINN) that combines deep learning wit...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.