An operator-theoretic approach to the Toda lattice equation

DOI10.1016/S0167-2789(98)00173-0zbMath0977.37042MaRDI QIDQ1808323

Cornelia Schiebold

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

\(N\)-soliton solutionsdiagonal operators

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Applications of operator theory to differential and integral equations (47N20)

Related Items (13)

Closed form Solutions to the Integrable Discrete Nonlinear Schrödinger Equation ⋮ A matrix Schrödinger approach to focusing nonlinear Schrödinger equations with nonvanishing boundary conditions ⋮ An operator method for finding exact solutions to vector Korteweg–de Vries equations ⋮ The Hasse-Weil Bound and Integrability Detection in Rational Maps ⋮ From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems ⋮ The Sylvester equation and the elliptic Korteweg-de Vries system ⋮ Dynamics of bright and dark multi-soliton solutions for two higher-order Toda lattice equations for nonlinear waves ⋮ Extended mixed function method and its application for solving two classic Toda lattice equations ⋮ Discretization of nonlinear evolution equations over associative function algebras ⋮ The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation ⋮ Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour ⋮ Matrix Solitons Solutions of the Modified Korteweg–de Vries Equation ⋮ Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions

Cites Work

• Theory of nonlinear lattices
• Limits of soliton solutions
• New classes of Toda soliton solutions
• Eigenvalue distribution of compact operators
• Tensor products and elementary operators.
• The nonabelian Toda lattice: Discrete analogue of the matrix Schrödinger spectral problem
• On realizations of solutions of the KdV equation by determinants on operator ideals
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