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Nonlinear Equations for Soliton Eigenfunctions Are the IST Integrable Equations

  • B. G. Konopelchenko
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

A starting and basic point of the inverse spectral transform (IST) method is the representation of the given nonlinear partial differential equation as the compatibility condition of some nontrivial linear system
$$\begin{array}{*{20}{c}} {{{L}_{1}}(U;\lambda )\Psi } \hfill & = \hfill & {0,} \hfill \\ {{{L}_{2}}(U;\lambda )\Psi } \hfill & = \hfill & 0 \hfill \\ \end{array}$$
(1)
where L 1 and L 2 are usually differential operators the coefficients of which depend on the field U(x,t), U x , U xx ,... and spectral parameter λ (see e.g. [1–4]). Integrable equation for U arises after the elimination of the eigenfunction Ψ from the system (1) [1–4].

Keywords

Compatibility Condition Nonlinear Integrable Equation mKdV Equation Eigenfunction Equation Linear Singular Integral Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin, Heidelberg 1990

Authors and Affiliations

  • B. G. Konopelchenko
    • 1
  1. 1.Institute of Nuclear PhysicsNovosibirskUSSR

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