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Fundam. Prikl. Mat., 2004, Volume 10, Issue 1, Pages 57–165 (Mi fpm756)  

This article is cited in 2 scientific papers (total in 2 papers)

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

A. V. Kiselevab

a Ivanovo State Power University
b Lecce University

Abstract: In this paper, we investigate algebraic and geometric properties of hyperbolic Toda equations $u_{xy}=\exp(Ku)$ associated with nondegenerate symmetrizable matrices $K$. A hierarchy of analogues of the potential modified Korteweg"– de Vries equation $u_t=u_{xxx}+u_x^3$ is constructed and its relationship 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 $\Psi_t=\boldsymbol i\Psi_{xx}+\boldsymbol if(|\Psi|)\Psi$ (multi-soliton complexes) are described.

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English version:
Journal of Mathematical Sciences (New York), 2006, 136:6, 4295–4377

Bibliographic databases:

UDC: 517.957+514.763.85

Citation: A. V. Kiselev, “Methods of geometry of differential equations in analysis of integrable models of field theory”, Fundam. Prikl. Mat., 10:1 (2004), 57–165; J. Math. Sci., 136:6 (2006), 4295–4377

Citation in format AMSBIB
\Bibitem{Kis04}
\by A.~V.~Kiselev
\paper Methods of geometry of differential equations in analysis of integrable models of field theory
\jour Fundam. Prikl. Mat.
\yr 2004
\vol 10
\issue 1
\pages 57--165
\mathnet{http://mi.mathnet.ru/fpm756}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2119753}
\zmath{https://zbmath.org/?q=an:1074.37033}
\elib{http://elibrary.ru/item.asp?id=9068295}
\transl
\jour J. Math. Sci.
\yr 2006
\vol 136
\issue 6
\pages 4295--4377
\crossref{https://doi.org/10.1007/s10958-006-0229-0}
\elib{http://elibrary.ru/item.asp?id=14654307}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33745663333}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kiselev A.V., Wolf T., “Classification of integrable super-systems using the SsTools environment”, Comput Phys Comm, 177:3 (2007), 315–328  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Kiselev, AV, “The spiral minimal surfaces and their Legendre and Weierstrass representations”, Differential Geometry and Its Applications, 26:1 (2008), 23  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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