Nonlocal integrable partners to generalized MKdV and two-dimensional Toda lattice equation in the formalism of a dressing method with quantized spectral parameter

DOI10.1007/BF02100008zbMath0739.35090MaRDI QIDQ1182053

S. Singh

Publication date: 27 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

symmetry equationsdressing techniquenonlocal Toda lattice

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)

Related Items (13)

Generalized ILW hierarchy: solutions and limit to extended lattice GD hierarchy ⋮ Liouville reflection operator, affine Yangian and Bethe ansatz ⋮ The dressing techniques for intermediate hierarchies ⋮ Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter ⋮ A spectral transform for the intermediate nonlinear Schrödinger equation ⋮ On the initial value problem for the modified Benjamin–Ono equation ⋮ On combinatorial expansion of the conformal blocks arising from AGT conjecture ⋮ Reflectionless Analytic Difference Operators II. Relations to Soliton Systems ⋮ Vertex operator representation of some quantum tori Lie algebras ⋮ Integrable structure, W-symmetry and AGT relation ⋮ Lifshitz scaling, microstate counting from number theory and black hole entropy ⋮ Nonlocal integrable equations from the mKP hierarchy ⋮ Dynamical systems on quantum tori Lie algebras

Cites Work

• Continuum analogues of contragredient Lie algebras. (Lie algebras with a Cartan operator and nonlinear dynamical systems)
• Generalized internal long waves equations: Construction, Hamiltonian structure, and conservation laws
• Lie algebras and equations of Korteweg-de Vries type
• Integrable nonlinear Klein-Gordon equations and Toda lattices
• Modifying Lax equations and the second Hamiltonian structure
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

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