Generating operators for integrable nonlinear evolution equations
Copyright policy )Generating operators for integrable nonlinear evolution equations
For linear problems which are associated with known, exactly integrable nonlinear evolution equations, one gives the corresponding integrodifferential Λ-operators. Relative to the expansions with respect to the elgenfunctions of Λ-operators, the method of the inverse scattering problem can be considered as the analog of the Fourier transform of linear problems, while the Λ-operators are the analogues of the differentiation operator. One considers the equations: Koteweg-de Vries, the nonlinear Schrodinger equations, the nonlinear Schrodinger equations with a derivative, the system of three waves, the matricial analog of the KdV equation, the Toda chain equation.
Hamilton's equations, generating operator, nonlinear differential equations, Applications of operator algebras to the sciences, Partial differential equations of mathematical physics and other areas of application, three wave system, Quantum scattering theory, Hamiltonian equation, Toda lattice equation, soliton theory, matrix Korteweg-de Vries equation, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds, linear spectral problems, inverse scattering method, hereditary symmetry, Korteweg-de Vries equation, Scattering theory for PDEs, nonlinear Schrödinger equation, derivative nonlinear Schrödinger equation
Hamilton's equations, generating operator, nonlinear differential equations, Applications of operator algebras to the sciences, Partial differential equations of mathematical physics and other areas of application, three wave system, Quantum scattering theory, Hamiltonian equation, Toda lattice equation, soliton theory, matrix Korteweg-de Vries equation, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds, linear spectral problems, inverse scattering method, hereditary symmetry, Korteweg-de Vries equation, Scattering theory for PDEs, nonlinear Schrödinger equation, derivative nonlinear Schrödinger equation
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