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.