Completeness of Derivatives of Squared Schrödinger Eigenfunctions and Explicit Solutions of the Linearized K<scp>d</scp>V Equation

DOI10.1137/0514051zbMath0554.35101OpenAlexW2007431505MaRDI QIDQ3217018

Publication date: 1983

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0514051

zbMATH Keywords

Cauchy problem Schrödinger equation superposition explicit formula scattering data linearized KdV equation

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Partial differential equations of mathematical physics and other areas of application (35Q99) Ordinary differential operators (34L99)

Related Items (17)

Perturbation theory for the Dirac equation in two-dimensional space ⋮ Perturbative analysis of wave interaction in nonlinear systems ⋮ Asymptotics of the first correction in the perturbation of the \(N\)-soliton solution of the KdV equation ⋮ Integrability and linear stability of nonlinear waves ⋮ Error propagation when approximating multi-solitons: The KdV equation as a case study ⋮ Cauchy problem for the linearized version of the Generalized Polynomial KdV equation ⋮ Linear stability of elastic 2-line solitons for the KP-II equation ⋮ Asymptotics of an integral that arises in the theory of perturbations of KdV solitons ⋮ The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation ⋮ Initial value problem of the linearized Benjamin–Ono equation and its applications ⋮ Perturbation of the Korteweg-de Vries soliton ⋮ Stability of elliptic solutions to the sinh-Gordon equation ⋮ Modal expansions and completeness relations for some time-dependent Schrödinger equations ⋮ Perturbation of a two-soliton solution of the Korteweg-de Vries equation in the case of close amplitudes ⋮ Numerical analysis on the generation, propagation and interaction of solitary waves by a harmonic polynomial cell method ⋮ Structure of linearization operators of the Korteweg-de Vries hierarchy equations expanded around single-soliton solutions ⋮ The orbital stability of the periodic traveling wave solutions to the defocusing complex modified Korteweg-de Vries equation

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