Results 91 to 100 of about 8,881 (223)
White-Noise-Driven KdV-Type Boussinesq System
MathematicsThe white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize features from both the ...
Aissa Boukarou +4 more
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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
The conservative Camassa–Holm flow with step‐like irregular initial data
Proceedings of the London Mathematical Society, Volume 130, Issue 5, May 2025.Abstract We extend the inverse spectral transform for the conservative Camassa–Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness‐type conditions at the other endpoint. The latter condition appears to be close to optimal in a certain sense for the well‐posedness of the conservative ...
Jonathan Eckhardt, Aleksey Kostenko
wiley +1 more source
On abundant new solutions of two fractional complex models
Advances in Difference Equations, 2020 We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg–de Vries equation (KdV) equation and the fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation).
Mostafa M. A. Khater, Dumitru Baleanu
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Superposition solutions to the extended KdV equation for water surface waves
, 2017 The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects.
Infeld, Eryk +2 more
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Foundations of Ghost Stability
Fortschritte der Physik, Volume 73, Issue 4, April 2025.Abstract The authors present a new method to analytically prove global stability in ghost‐ridden dynamical systems. The proposal encompasses all prior results and consequentially extends them. In particular, it is shown that stability can follow from a conserved quantity that is unbounded from below, contrary to expectation.
Verónica Errasti Díez +2 more
wiley +1 more source
Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
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Error estimates for a physics-informed neural network in solving KdV equations
Machine Learning: Science and TechnologyThis 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
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the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method
Tikrit Journal of Pure ScienceThe 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 +2 more
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Observations of the Bottom Boundary Layer Beneath the World's Largest Internal Solitary Waves
Journal of Geophysical Research: Oceans, Volume 130, Issue 3, March 2025.Abstract Measurements in the South China Sea reveal the structure of the bottom boundary layer beneath onshore propagating highly nonlinear internal solitary waves of depression. Offshore directed free stream velocities beneath 13 waves with durations of 10–20 min and velocities up to 1.4 m/s are consistent with the solitary wave solution to the ...
J. H. Trowbridge +7 more
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