Methods of geometry of differential equations in analysis of the integrable field theory models
Abstract
Description
In this paper, we investigate the algebraic and geometric properties of the hyperbolic Toda equations $u_{xy}=\exp(Ku)$ associated with nondegenerate symmetrizable matrices $K$. A hierarchy of analogs to the potential modified Korteweg-de Vries equation $u_t=u_{xxx}+u_x^3$ is constructed, and its relation with the hierarchy for the Korteweg-de Vries equation $T_t=T_{xxx}+TT_x$ is established. Group-theoretic structures for the dispersionless (2+1)-dimensional Toda equation $u_{xy}=\exp(-u_{zz})$ are obtained. Geometric properties of the multi-component nonlinear Schrödinger equation type systems $Ψ_t = iΨ_{xx} + i f(|Ψ|) Ψ$ (multi-soliton complexes) are described.
LaTeX2e, 134 pages, no figures, uses diagrams.tex. Submitted to: Fundamental'naya i Prikladnaya Matematika/J. Math. Sci
LaTeX2e, 134 pages, no figures, uses diagrams.tex. Submitted to: Fundamental'naya i Prikladnaya Matematika/J. Math. Sci