NDLI: N-wave soliton solution on a generic background for KPI equation

Content Provider	IEEE Xplore Digital Library
Author	Boiti, M. Pempinelli, F. Prinari, B. Pogrebkov, A.K.
Copyright Year	1999
Description	Author affiliation: Dipt. di Fisica, Lecce Univ., Italy (Boiti, M.)
Abstract	We try to generalize the inverse scattering transform (IST) for the Kadomtsev-Petviashvili (KPI) equation to the case of potentials with "ray" type behavior, that is non-decaying along a finite number of directions in the plane. We present here the special but rather wide subclass of such potentials obtained by applying recursively N binary Backlund transformations to a decaying potential. We start with a regular rapidly decaying potential for which all elements of the direct and inverse problem are given. We introduce an exact recursion procedure for an arbitrary number of binary Backlund transformations and corresponding Darboux transformations for Jost solutions and solutions of the discrete spectrum. We show that Jost solutions obey modified integral equations and present their analytical properties. We formulate conditions of reality and regularity of the potentials constructed by these means and derive spectral data of the transformed Jost solutions. Finally we solve the recursion procedure getting a solution which describes N solitons superimposed to a generic background.
Starting Page	167
Ending Page	175
File Size	300393
Page Count	9
File Format	PDF
ISBN	5799701569
DOI	10.1109/DD.1999.816197
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-06-01
Publisher Place	Russia
Access Restriction	Subscribed
Rights Holder	Day on Diffraction, Fac. Of Phys., SPbU
Subject Keyword	Solitons Integral equations Inverse problems H infinity control Green's function methods Diffraction
Content Type	Text
Resource Type	Article

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