Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation
type: Item
instance of: scholarly article
title: Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation
published in: Khayyam Journal of Mathematics
publication date: 2025-01-28T00:00:00Z
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 7975480
zbMATH Keywords: bilinear neural network method
zbMATH Keywords: KdV equation
zbMATH Keywords: traveling wave solution
zbMATH Keywords: Hirota bilinear form
MaRDI profile type: Publication
cites work: A generalized auxiliary equation method and its applications
cites work: Q3994822
cites work: Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials
cites work: A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
cites work: Q4395060
cites work: Nonsingular positon and complexiton solutions for the coupled KdV system
cites work: Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method
cites work: Topological soliton solutions for three shallow water waves models
cites work: Exact solutions to the combined KdV and mKdV equation
cites work: Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method
cites work: New exact solutions for the KdV equation with higher order nonlinearity by using the variational method
cites work: An extended modified KdV equation and its Painlevé integrability
cites work: Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
cites work: Dynamical behaviors of different wave structures to the Korteweg-de Vries equation with the Hirota bilinear technique
cites work: Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
cites work: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation
cites work: Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation
cites work: Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method
cites work: Exact solutions of a KdV equation hierarchy with variable coefficients
cites work: The exact solutions to the complex KdV equation
cites work: Complexiton solutions to soliton equations by the Hirota method
DOI: 10.22034/KJM.2024.396918.2865
description: scientific article; zbMATH DE number 7975480