Jordan algebras and integrable systems

zbMath0840.35099MaRDI QIDQ1337912

S. I. Svinolupov

Publication date: 5 December 1994

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

Korteweg-de Vries equationsine-Gordon equationMiura mapJordan analogsmodified Koteweg-de Vries equationpotential mKdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70) Simple, semisimple Jordan algebras (17C20)

Related Items (19)

Frobenius manifolds and Frobenius algebra-valued integrable systems ⋮ Three Fibonacci-chain aperiodic algebras ⋮ Multi-soliton solutions of the generalized variable-coefficient Bogoyavlenskii equation ⋮ Integrability and exact solutions of a two-component Korteweg-de Vries system ⋮ New examples of the auto-Bäcklund transformations and nonlinear superposition formulas for vector evolution systems ⋮ Noncommutative integrable systems of hydrodynamic type ⋮ Multi-soliton solutions for the three-coupled KdV equations engendered by the Neumann system ⋮ Symmetry reductions, exact solutions and conservation laws of a new coupled KdV system ⋮ On the solutions and conservation laws of a coupled KdV system ⋮ New integrable systems of derivative nonlinear Schrödinger equations with multiple components ⋮ Integrable KdV systems: Recursion operators of degree four ⋮ Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy ⋮ Differential substitutions for non-Abelian equations of KdV type ⋮ Contractions of 2-dimensional Jordan algebras ⋮ Integrability of a coupled KdV system: Painlevé property, Lax pair and Bäcklund transformation ⋮ Prolongation structures of a generalized coupled Korteweg-de Vries equation and Miura transformation ⋮ Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)^th KdV Hierarchy ⋮ Multi-component generalizations of mKdV equation and nonassociative algebraic structures ⋮ New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

Cites Work

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• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Resonance regions for Mathieu type dynamical systems on a torus
• Bifurcations and stability of families of diffeomorphisms
• Attractors on an N-torus: Quasiperiodicity versus chaos
• Pseudocharacters on the group \(\text{SL}(2,\mathbb{Z})\)
• Scaling of the Arnold tongues
• Resonance Zones in Two-Parameter Families of Circle Homeomorphisms
• Rotation Sets of Toral Flows
• Rotation Sets for Maps of Tori
• Resonance regions for families of torus maps
• Small denominators. I. Mappings of the circumference onto itself

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