Results 81 to 90 of about 8,902 (211)

Closed-form solutions and conservation laws of a generalized Hirota–Satsuma coupled KdV system of fluid mechanics

Open Physics, 2021
In this article, a generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system is investigated from the group standpoint. This system represents an interplay of long waves with distinct dispersion correlations.
Khalique Chaudry Masood
doaj   +1 more source

ANALYTICAL SOLUTION OF KORTEWEG-DE VRIES EQUATION (KdV) BY LAPLACE DECOMPOSITION METHOD

, 2021
The target of this paper is to apply a Laplace decomposition method (LDM) to obtain analytical solution of KdV equation and to discuss the efficiency of the solution of KdV equation obtained by the LDM compared with the exact solution. As a result, the explicit solution to a generalized Korteweg–de Vries equation (KdV for short) with initial condition ...
openaire   +2 more sources

Novel Nonlinear Dynamical Solutions to the (2 + 1)‐Dimensional Variable Coefficients Equation Arise in Oceanography

Engineering Reports, Volume 7, Issue 6, June 2025.
This study explores novel nonlinear dynamical solutions to the (2 + 1)‐dimensional variable coefficient equation in oceanography. Using the Hirota bilinear method, we derive multi‐soliton, M‐lump, and hybrid wave solutions, revealing collision phenomena and their physical significance in nonlinear fluid dynamics and mathematical physics.
Hajar F. Ismael, Tukur Abdulkadir Sulaiman, Harivan R. Nabi, Shams Forruque Ahmed   +3 more
wiley   +1 more source

Error estimates for a physics-informed neural network in solving KdV equations

Machine Learning: Science and Technology
This paper aims to provide error bounds on physics-informed neural network (PINN) in solving Korteweg–de Vries (KdV) equations. We prove that a neural network equipped with two hidden layers and the tanh activation function can reduce the partial ...
Jia Guo, Ziyuan Liu, Chenping Hou
doaj   +1 more source

the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method

Tikrit Journal of Pure Science
The aim of this article is to propose an efficient hybrid transform iteration method that combines the homotopy perturbation approach, the variational iteration method, and the Aboodh transform forsolving various partial differential equations.
Ruaa Shawqi Ismael, Ali Al -Fayadh, Saad M. Salman   +2 more
doaj   +1 more source

Propagation of weakly nonlinear axial waves of nanorods embedded in a viscoelastic medium

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 6, June 2025.
Abstract Nonlinear equations play a fundamental role in explaining complex systems in science and technology, particularly in the field of wave propagation. Nonlocal elasticity theory is a general method for analyzing nanostructures at the nanoscale. The current work utilizes Eringen's nonlocal constitutive equations to solve the nonlinear equations of
Guler Gaygusuzoglu, Zehra Pinar Izgi, Aydin Ozmutlu   +2 more
wiley   +1 more source

Numerical Solitons of Generalized Korteweg-de Vries Equations

, 2005
We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We
Camassa, Fokas, Gardner, Houde Han, Rosenau, Rosenau, Zabusky, Zhenli Xu   +7 more
core   +2 more sources

N$N$‐Soliton Matrix mKdV Solutions: Some Special Solutions Revisited

Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.
ABSTRACT In this article, a general solution formula is derived for the d×d${\sf d}\times {\sf d}$‐matrix modified Korteweg–de Vries equation. Then, a solution class corresponding to special parameter choices is examined in detail. Roughly, this class can be described as N$N$‐solitons (in the sense of Goncharenko) with common phase matrix. It turns out
Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold   +2 more
wiley   +1 more source

Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method

Journal of Applied Mathematics, 2012
The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series ...
Mojtaba Nazari, Faisal Salah, Zainal Abdul Aziz, Merbakhsh Nilashi   +3 more
doaj   +1 more source

The Painlev\'e analysis for N=2 super KdV equations

, 2001
The Painlev\'e analysis of a generic multiparameter N=2 extension of the Korteweg-de Vries equation is presented. Unusual aspects of the analysis, pertaining to the presence of two fermionic fields, are emphasized.
Bourque, S., Mathieu, P.
core   +1 more source