Soliton solutions to zakharov-shabat systems by the reduction method

J. Harnad, Y. Saint-Aubin, S. Shnider

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2 Scopus citations

Abstract

This chapter discusses soliton solutions to Zakharov–Shabat systems by the reduction method. It is shown how the Zakharov–Mikhailov–Shabat “dressing method” for the construction of multi-soliton solutions to generalized Zakharov–Shabat systems may be combined with the “reduction method” of Mikhailov to obtain multi-soliton solutions for all algebraically reduced systems. The results are illustrated with two simple examples: (1) the S2sigma model and (2) the Thirring model. The reduction method of Mikhailov consists of restricting the general system by imposing constraints in the form of invariance under a finite group of automorphisrns. The multi-soliton solutions are described in the chapter.

Original languageEnglish
Pages (from-to)423-432
Number of pages10
JournalNorth-Holland Mathematics Studies
Volume97
Issue numberC
DOIs
StatePublished - 1 Jan 1984
Externally publishedYes

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