N-soliton formulae for the intermediate nonlinear Schrodinger equation

Authors
Citation
Y. Matsuno, N-soliton formulae for the intermediate nonlinear Schrodinger equation, INVERSE PR, 17(3), 2001, pp. 501-514
Citations number
18
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
INVERSE PROBLEMS
ISSN journal
0266-5611 → ACNP
Volume
17
Issue
3
Year of publication
2001
Pages
501 - 514
Database
ISI
SICI code
0266-5611(200106)17:3<501:NFFTIN>2.0.ZU;2-7
Abstract
A direct proof is given to the N-soliton solution of the intermediate nonli near Schrodinger (INLS) equation describing envelope waves. The proof relie s only on an elementary theory of determinants and knowledge of the inverse scattering transform method is not required. In particular, when the N-sol iton solution is substituted into the system of bilinear equations for the INLS equation, the system is found to reduce to Jacobi's formula for determ inants. A special class of N-soliton solutions is also presented which is e xpressed in terms of exponential functions. In the deep-water limit, the so lution reduces to the algebraic N-soliton solution of a nonlocal NLS equati on with the Hilbert kernel whereas in the shallow-water limit, the solution reduces to the N-soliton solution of the defocusing NLS equation.