We obtain the nondegenerate one-and two-soliton solutions of the nonlocal nonlinear
Schrödinger equation by using the nonstandard Hirota method. This unconventional method …

Interference wave is an important research target in the field of navigation, electromagnetic
and earth science. In this work, the nonlinear property of neural network is used to study the …

In this work, bilinear residual network method is proposed to solve nonlinear evolution
equations. The activation function in final layer of deep neural network cannot interact with …

In this work, some new test functions are constructed by setting generalized activation
functions in different artificial network models. Bilinear neural network method is introduced …

Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic
flow, plasma astrophysics and ocean dynamics. In this paper, a (2+ 1)-dimensional …

We use the physics-informed neural network to solve a variety of femtosecond optical soliton
solutions of the high-order nonlinear Schrödinger equation, including one-soliton solution …

Under investigation in this paper is the (2+ 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-
Sawada-like (CDGKS-like) equation. Based on bilinear neural network method, the …

It is well known that most classical test functions to solve nonlinear partial differential
equations can be constructed via single hidden layer neural network model by using …

This paper investigates data-driven forward–inverse problems associated with the variable
coefficients Hirota (VC-Hirota) equation using the physics-informed neural network (PINN) …

This article investigates a nonlinear fifth-order partial differential equation (PDE) in two-
mode waves. The equation generalizes two-mode Sawada-Kotera (tmSK), two-mode Lax …