Auto-Backlund transformations and superposition formulas for solutions of Drinfeld-Sokolov systems

M, Yu Balakhnev; Dmitry Demskoy

doi:10.1016/j.amc.2012.09.057

Auto-Backlund transformations and superposition formulas for solutions of Drinfeld-Sokolov systems

M, Yu Balakhnev, Dmitry Demskoy

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The paper is devoted to constructing Auto-Backlund transformations (ABT) and superposi-tion formulas for the solutions of the Drinfeld-Sokolov (DS) systems. The transformationsare derived from pairs of differential substitutions relating different systems of the DS type.The nonlinear superposition formulas for solutions of the DS systems are obtained from theassumption of commutativity of the Bianchi diagram. We indicate a seed solution for eachsystem which can be used to generate multi-soliton solutions. As an application of thesuperposition formulas we construct two-soliton solutions for each of the DS systems.

Original language	English
Pages (from-to)	3625-3637
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	219
Issue number	8
DOIs	https://doi.org/10.1016/j.amc.2012.09.057
Publication status	Published - Dec 2012

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title = "Auto-Backlund transformations and superposition formulas for solutions of Drinfeld-Sokolov systems",

abstract = "The paper is devoted to constructing Auto-Backlund transformations (ABT) and superposi-tion formulas for the solutions of the Drinfeld-Sokolov (DS) systems. The transformationsare derived from pairs of differential substitutions relating different systems of the DS type.The nonlinear superposition formulas for solutions of the DS systems are obtained from theassumption of commutativity of the Bianchi diagram. We indicate a seed solution for eachsystem which can be used to generate multi-soliton solutions. As an application of thesuperposition formulas we construct two-soliton solutions for each of the DS systems.",

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AB - The paper is devoted to constructing Auto-Backlund transformations (ABT) and superposi-tion formulas for the solutions of the Drinfeld-Sokolov (DS) systems. The transformationsare derived from pairs of differential substitutions relating different systems of the DS type.The nonlinear superposition formulas for solutions of the DS systems are obtained from theassumption of commutativity of the Bianchi diagram. We indicate a seed solution for eachsystem which can be used to generate multi-soliton solutions. As an application of thesuperposition formulas we construct two-soliton solutions for each of the DS systems.

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Auto-Backlund transformations and superposition formulas for solutions of Drinfeld-Sokolov systems

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