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Methods of geometry of differential equations in analysis of the integrable field theory models | | Arthemy V. Kiselev
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17 Jun 2004 | | Journal: | Fundamental’naya i Prikladnaya Matematika 10 (2004) n.1 "Geometry of Integrable Models", 57-165. | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | 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 $Psi_t = iPsi_{xx} + i f(|Psi|) Psi$ (multi-soliton complexes) are described. | | Source: | arXiv, nlin.SI/0406036 | | Services: | Forum | Review | PDF | Favorites | |
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