Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. [PDF]
, 2012 The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the ...
Blower, Gordon
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On tau functions associated with linear systems [PDF]
, 2012 \noindent {\bf Abstract} This paper considers the Fredholm determinant $\det (I-\Gamma_x)$ of a Hankel integral operator on $L^2(0, \infty )$ with kernel $\phi (s+t+2x)$, where $\phi$ is a matrix scattering function.
Samantha L. Newsham +3 more
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A note on travelling-wave solutions to Lax's seventh-order KdV equation [PDF]
, 2009 Ganji and Abdollahzadeh [D.D. Ganji, M. Abdollahzadeh, Appl. Math. Comput.206 (2008) 438{444] derived three supposedly new travelling-wave solutions to Lax's seventh-order KdV equation. Each solution was obtained by a different method.
Parkes, E.J.
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A note on solitary travelling-wave solutions to the transformed reduced Ostrovsky equation [PDF]
, 2010 Two recent papers are considered in which solitary travelling-wave solutions to the transformed reduced Ostrovsky equation are presented.
Parkes, E.J.
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Multiscale expansion and integrability properties of the lattice potential KdV equation [PDF]
, 2008 We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schrödinger
Decio Levi +10 more
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Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method [PDF]
, 2009 The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution.
Abbasbandy, S., Parkes, E.J.
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Jordan manifolds and dispersionless KdV equations [PDF]
, 2000 Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order ...
I. A. B. Strachan +2 more
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Exact solutions for STO and (3+1)-dimensional KdV-ZK equations using G′G2-expansion method
Results in Physics, 2017 This article deals with finding some exact solutions of nonlinear fractional differential equations (NLFDEs) by applying a relatively new method known as G′G2-expansion method.
Sadaf Bibi +4 more
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On a Schwarzian PDE associated with the KdV hierarchy [PDF]
, 2000 We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy.
Hone, A. N. W. +8 more
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ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD
Barekeng, 2023 In this research we discussed about the solution of the KdV equation using Homotopy Perturbation method. The KdV equation that describing water wave equation solved by using the mixing method between Homotopy and Perturbation method.
Mashuri Mashuri +2 more
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