Recursion Operators for N×N Matrix Nonlinear Evolution Equations
Naruyoshi Asano,Yusuke Kato +1 more
TLDR
In this article, the theory d'Ablowitz-kaup-Newell-Segur for le systeme matriciel N×N, on obtient l'equation d'evolution non lineaire generale associee, dans laquelle l'operateur de recurrence est directement deduit de la condition d'integrabilite.Abstract:
Dans la theorie d'Ablowitz-Kaup-Newell-Segur pour le systeme matriciel N×N, on obtient l'equation d'evolution non lineaire generale associee, dans laquelle l'operateur de recurrence est directement deduit de la condition d'integrabilite. On considere la loi de superposition non lineaire et les symetries associees aux equations d'evolutionread more
Citations
More filters
Journal ArticleDOI
Bi‐Hamiltonian structures of the coupled AKNS hierarchy and the coupled Yajima–Oikawa hierarchy
TL;DR: In this article, the second Hamiltonian structure of the Yajima-Oikawa hierarchy is shown to be a Dirac reduction of the sl(3) current algebra, while the latter is related to the classical W( 3)4 algebra.
Journal ArticleDOI
Some connections between inverse scattering and solution hierarchies
TL;DR: In this paper, asymptotic expressions for AKNS wave matrices involving tau functions based on continuous spectrum are related to the appropriate dressing gauge transformations via hierarchy considerations and asymptic expressions for continuous spectrum situations.
Journal ArticleDOI
Hierarchies of evolution equations associated with certain symmetric spaces
TL;DR: In this article, Hierarchies of evolution equations associated with Hermitian symmetric spaces are presented, and the obtained evolution equations include generalized nonlinear Schrodinger equations, which are obtained by extending the Lie algebra in the Ablowitz-Kaup-Newell-Segur scheme from sl(2,C) to more general one.
References
More filters
Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Journal ArticleDOI
Scattering and inverse scattering for first order systems
Richard Beals,Ronald R. Coifman +1 more
TL;DR: In this article, the authors present resultats sur la theorie analytique des problemes de diffusion and de diffusion inverse for des systemes generalises AKNS. But they do not consider diffusion in general.
Journal ArticleDOI
Application of hereditary symmetries to nonlinear evolution equations
TL;DR: In this paper, the evolution equation ur = K(u), where the subscript t denotes the time derivative, is considered and it is shown that K: E −+E (possibly nonlinear) is differentiable.
Journal ArticleDOI
On the spectral theory of the integro-differential operator a generating nonlinear evolution equations
TL;DR: In this article, the main steps of constructing the spectral theory of the integro-differential operator A generating a class of exactly soluble nonlinear evolution equations (NLEE) related to the linear matrix first-order problem L are outlined.
Related Papers (5)
Solving homogeneous linear differential equations in terms of second order linear differential equations
Collapse in the n‐Dimensional Nonlinear Schrödinger Equation—A Parallel with Sundman's
F. H. Berkshire,John Gibbon +1 more
Solvability of some operator equations and periodic solutions of nonlinear functional differential equations
A Cañada,P Martinez-Amores +1 more