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The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.

Integration of the EPDiff equation by particle methods

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that is well-suited for this class of solutions and...

Integration of the EPDiff equation by particle methods∗∗∗∗∗∗

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Integration of the perturbated Jacobi problem.

Dragović, Vladimir (1998)

Publications de l'Institut Mathématique. Nouvelle Série

Invariance of the Gibbs measure for the Benjamin–Ono equation

Yu Deng (2015)

Journal of the European Mathematical Society

In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than $L^{2}$ , extending the $L^{2}$ well-posedness result of Molinet [20].

Isometric immersions and the generalized Laplace and elliptic sinh-Gordon equations.

M. Dajczer, Ruy Tojeiro (1995)

Journal für die reine und angewandte Mathematik

Isometric immersions of domains of Lobachevski space in Euclidean spaces

Zapiski naucnych seminarov POMI

Isometric immersions of space forms and soliton theory.

Dirk Ferus, Franz Pedit (1996)

Mathematische Annalen

Ito equation as a geodesic flow on $\hat{{Diff}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$

Partha Guha (2000)

Archivum Mathematicum

The Ito equation is shown to be a geodesic flow of $L^{2}$ metric on the semidirect product space $\hat{{𝐷𝑖𝑓𝑓}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$ , where ${𝐷𝑖𝑓𝑓}^{s} (S^{1})$ is the group of orientation preserving Sobolev $H^{s}$ diffeomorphisms of the circle. We also study a geodesic flow of a $H^{1}$ metric.

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