Results 41 to 50 of about 1,267 (106)
Chains of KP, semi‐infinite 1‐Toda lattice hierarchy and Kontsevich integral
Journal of Applied Mathematics, Volume 1, Issue 4, Page 175-193, 2001., 2001 There are well‐known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1‐Toda lattice hierarchy.
L. A. Dickey
wiley +1 more source
B\"acklund-Darboux Transformations and Discretizations of Super KdV Equation [PDF]
, 2014 For a generalized super KdV equation, three Darboux transformations and the corresponding B\"acklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.
Liu, Qing Ping, Xue, Ling-Ling
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Three‐dimensional Korteweg‐de Vries equation and traveling wave solutions
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 6, Page 379-384, 2000., 2000 The three‐dimensional power Korteweg‐de Vries equation [ut+unux+uxxx] x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n = 1 and n = 2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson′s summation ...
Kenneth L. Jones
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Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter [PDF]
, 2006 We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and nonintegrable equations ...
Kordyukova, Svetlana
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 643-648, 1999., 1999 The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions.
Kenneth L. Jones, Yunkai Chen
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On the support of solutions to the Zakharov-Kuznetsov equation [PDF]
, 2010 In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation that have compact support for two different times are identically zero.Comment: Version of Dec 17/2010 contains simpler proof of Theorem 1.3 and new ...
Bustamante, Eddye +2 more
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Addendum to a paper of Craig and Goodman
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 825-827, 1994., 1994 In [1], Craig and Goodman develop the geometrical optics solution of the linearized Korteweg‐deVries equation away from caustic, or turning, points. Here we develop an analogous solution valid at caustic points.
Arthur D. Gorman
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Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain
Journal of Partial Differential Equations, 2018 In this paper, we study exact controllability and feedback stabilization for the distributed parameter control system described by high-order KdV equation posed on a periodic domain T with an internal control acting on an arbitrary small nonempty ...
Z. Meng
semanticscholar +1 more source
Soliton solution of the osmosis K(2, 2) equation
, 2009 In this Letter, by using the bifurcation method of dynamical systems, we obtain the analytic expressions of soliton solution of the osmosis K(2, 2) equation.Comment: 8 ...
Biswas +10 more
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On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation [PDF]
, 2006 Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa--Holm model.
Aratyn, H. +2 more
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