Geometry and multidimensional soliton equations

DOI10.1007/BF02557332zbMath0981.37022MaRDI QIDQ1567797

A. K. Danlybaeva, Ratbay Myrzakulov, Gulgasyl Nugmanova

Publication date: 27 May 2002

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Curves in Euclidean and related spaces (53A04)

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Cites Work

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• Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation
• Benney equations and quasiclassical approximation in the method of the inverse problem
• An elementary geometric characterization of the integrable motions of a curve
• A \((2+1)\)-dimensional integrable spin model: geometrical and gauge equivalent counterpart, solitons and localized coherent structures.
• Method for Solving the Korteweg-deVries Equation
• Gauge equivalence between -dimensional continuous Heisenberg ferromagnetic models and nonlinear Schrödinger-type equations
• Solitons on moving space curves
• On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schrödinger equations
• Integrability and the motion of curves
• Some integrable hierarchies in (2+1) dimensions and their twistor description
• Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions
• A soliton on a vortex filament