Results 71 to 80 of about 22,064 (260)
Soliton fission and fusion of a new two-component Korteweg–de Vries (KdV) equation
Computers & Mathematics with Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yong, Xuelin +2 more
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An operator valued extension of the super Korteweg–de Vries equations [PDF]
, 2000 An extension of the super Korteweg–de Vries (KdV) integrable system in terms of operator valued functions is obtained. Following the ideas of Gardner, a general algebraic approach for finding the infinitely many conserved quantities of integrable systems
S. Andrea, A. Sotomayor, A. Restuccia
semanticscholar +1 more source
Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
wiley +1 more source
A Note on the Fractional Generalized Higher Order KdV Equation
Journal of Function Spaces, 2018 We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations ...
Yongyi Gu
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Alexandria Engineering Journal, 2023 Non-linear evolution equations play a prominent role in describing a wide range of phenomena in optical fibers, fluid dynamics, electromagnetic radiation, plasma and solid state physics.
Mubashir Qayyum +4 more
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Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor +5 more
wiley +1 more source
An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation [PDF]
Proceedings of the National Academy of Sciences, 1998 This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way. We present, in particular, an algorithm, to obtain the support of the Riemann-Hilbert problem for leading asymptotics. Applying this extended method to small dispersion KdV (Korteweg-de Vries) equation, we (
Deift, P., Venakides, S., Zhou, X.
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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
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The solution of fractional-order system of KdV equations with exponential-decay kernel
Results in Physics, 2022 This study uses efficient techniques to evaluate a non-linear system of Korteweg–de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method.
Mohammad Alshammari +3 more
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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