Results 91 to 100 of about 8,902 (211)
Quasilinear Differential Constraints for Parabolic Systems of Jordan‐Block Type
Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.ABSTRACT We prove that linear degeneracy is a necessary conditions for systems in Jordan‐block form to admit a compatible quasilinear differential constraint. Such condition is also sufficient for 2×2$2\times 2$ systems and turns out to be equivalent to the Hamiltonian property.
Alessandra Rizzo, Pierandrea Vergallo
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The KdV hierarchy: universality and a Painleve transcendent
, 2011 We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the ...
Claeys, T., Grava, T.
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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
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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
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, 2001 Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that about one hundred
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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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KdV-type equations linked via Baecklund transformations: remarks and perspectives
, 2018 Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations.
Carillo, Sandra
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Lax representation with first-order operators for new nonlinear Korteweg – de Vries type equations
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. In this work, a new representation is constructed for equations of the Korteweg – de Vries (KdV) type. The proposed approach allows to obtain a universal Lax representation for a set of nonlinear partial differential equations, for which ...
V.M. Zhuravlev, V.M. Morozov
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Shallow water cnoidal wave interactions [PDF]
Nonlinear Processes in Geophysics, 1994 The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered.
A. R. Osborne
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