The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients [PDF]
, 2006 The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable.
Kobayashi, Tadashi, Toda, Kouichi
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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
About seismic tomography algorithm in the prediction of geological dislocations in coal seams
Горные науки и технологии, 2018 An algorithm for processing of crosshole seismic survey data enabling recognizing the type and evaluate the characteristics of geological anomalies using a system of criteria is described.
A. V. Antsiferov +4 more
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Gardner's deformations of the Boussinesq equations
, 2006 Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these
Karasu, Atalay, Kiselev, Arthemy V.
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High order multiscale analysis of discrete integrable equations [PDF]
Open Communications in Nonlinear Mathematical PhysicsIn this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions
Rafael Hernandez Heredero +2 more
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Rogue waves of the Fokas-Lenells equation
, 2012 The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schr\"odinger (NLS ...
He, Jingsong +2 more
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Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation
Advances in Nonlinear AnalysisIn this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the
Shan Minjie +3 more
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Evidence for the Nonintegrability of a Water Wave Equation in 2+1 Dimensions
, 2004 We provide evidence of the nonintegrability of a recently proposed model for water waves in 2+1 dimensions: we show that under a nonlinear time transformation, a certain reduction of this partial differential equation is mapped to an ordinary ...
P. R. Gordoa +2 more
semanticscholar +1 more source
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems [PDF]
, 2015 Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems.
Santoprete, Manuele
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From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators
, 2013 In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element.
A. Alexandrov +35 more
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