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

M. Boiti, F. Pempinelli, B. Prinari, A. K. Pogrebkov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We try to generalize the IST for 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 Bicklnnd 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 Darbonx 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.

Original languageEnglish
Title of host publicationInternational Seminar
Subtitle of host publicationDay on Diffraction - Proceedings
EditorsV.E. Grikuro, V.M. Babic, I.V. Androno, V.S. Buldyrev, A.P. Kiselev
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages9
ISBN (Electronic)5799701569, 9785799701567
Publication statusPublished - 1999
EventInternational Seminar: Day on Diffraction, IS-DoD 1999 - St. Petersburg, Russian Federation
Duration: 1 Jun 19993 Jun 1999

Publication series

NameInternational Seminar: Day on Diffraction - Proceedings


ConferenceInternational Seminar: Day on Diffraction, IS-DoD 1999
Country/TerritoryRussian Federation
CitySt. Petersburg


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