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Solitons and inverse scattering transform. (English) Zbl 1086.35085

Clemence, Dominic P. (ed.) et al., Mathematical studies in nonlinear wave propagation. Proceedings of the NSF-CBMS regional research conference, Greensboro, NC, USA, May 15–19, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3349-9/pbk). Contemporary Mathematics 379, 47-62 (2005).
Summary: A review of the inverse scattering transform is presented in solving initial-value problems for nonlinear evolution equations such as the Korteweg-de Vries equation. The derivation of such equations is illustrated by using the Lax method and the AKNS method. The inverse scattering problem is outlined for the one-dimensional Schrödinger equation, and the time evolution of the corresponding scattering data is given. Soliton solutions to the Korteweg-de Vries equation are explicitly written.
For the entire collection see [Zbl 1069.35002].

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q51 Soliton equations
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