Methods of geometry of differential equations in analysis of the integrable field theory models

Arthemy V. Kiselev

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arXiv · nlin/0406036

Methods of geometry of differential equations in analysis of the integrable field theory models

Arthemy V. Kiselev

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Abstract

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.

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Arthemy V. Kiselev. 2004-06-17. Methods of geometry of differential equations in analysis of the integrable field theory models. https://arxiv.org/abs/nlin/0406036

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