Results 71 to 80 of about 453 (182)
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
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley +1 more source
Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12427-12439, August 2025.ABSTRACT The Ostrovsky equation models long, weakly nonlinear waves, explaining the propagation of surface and internal waves in a rotating fluid. The study focuses on the generalized Ostrovsky equation. Introduced by Levandosky and Liu, this equation demonstrates the existence of solitary waves through variational methods.
Sol Sáez
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 +3 more
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
Emergence of Coupled Korteweg–de‐Vries Equations in m$m$ Fields
Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT The Korteweg–de‐Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi‐component systems relevant for multi‐species fluids and cold atomic mixtures. We present a general framework in which a family of multi‐component KdV (mcKdV) equations naturally arises from a broader mathematical structure
Sharath Jose +2 more
wiley +1 more source
Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEs
Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup ...
Alexey V. Bolsinov +2 more
wiley +1 more source
Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation
CoRRPhysics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration. This paper introduces a \emph{structure-preserving PINN} framework for the nonlinear Korteweg--de Vries (KdV ...
Victory Obieke, Emmanuel Oguadimma
openaire +2 more sources
Nonlinear inference capacity of fiber‐optical extreme learning machines
Nanophotonics, Volume 14, Issue 16, Page 2749-2760, August 2025.Abstract The intrinsic complexity of nonlinear optical phenomena offers a fundamentally new resource to analog brain‐inspired computing, with the potential to address the pressing energy requirements of artificial intelligence. We introduce and investigate the concept of nonlinear inference capacity in optical neuromorphic computing in highly nonlinear
Sobhi Saeed +5 more
wiley +1 more source
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 +3 more
wiley +1 more source