Generalised Inverse Scattering for a Linear PDE Associate to KdV

DOI

10.2991/jnmp.2005.12.s1.46How to use a DOI?

Abstract

Inverse Scattering methods for solving integrable nonlinear p.d.e. found their limits as soon as one tried to solve with them new boundary value problems. However, some of these problems, e.g. the quarter-plane problem, can be solved (e.g. by Fokas linear methods), for related linear p.d.e., (e.g. LKdV). It is shown here that a nonlinear algebraic inverse scattering method, which we already applied to nonlinear KdV, but with only partial results, gives the full solution of the quarter-plane problem of another linear p.d.e. associated to KdV. The method makes use of generalised Lax equations and their solutions.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - P.C. Sabatier
PY  - 2005
DA  - 2005/01/01
TI  - Generalised Inverse Scattering for a Linear PDE Associate to KdV
JO  - Journal of Nonlinear Mathematical Physics
SP  - 599
EP  - 613
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.46
DO  - 10.2991/jnmp.2005.12.s1.46
ID  - Sabatier2005
ER  -