American Institute of Mathematical Sciences

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2009, 2009(Special): 678-690. doi: 10.3934/proc.2009.2009.678

Noncommutative AKNS systems and multisoliton solutions to the matrix sine-gordon equation

Cornelia Schiebold 1,

1. 

Department of Natural Sciences, Engineering and Mathematics, Mid Sweden University, S-851 70 Sundsvall, Sweden

Received  June 2008 Revised  April 2009 Published  September 2009

The main result is a very general solution formula for the noncommutative AKNS system, extending work by Bauhardt and Pöppe. As an application, we construct for the matrix sine-Gordon equation $N$-soliton solutions analogous to the multisoliton solutions for the KdV equation due to Goncharenko.
Keywords: operator equations, Noncommutative integrable systems, matrix soliton solutions.
Mathematics Subject Classification: Primary: 35Q51, 47J25, 35C05; Secondary: 35Q53, 35Q55.
Citation: Cornelia Schiebold. Noncommutative AKNS systems and multisoliton solutions to the matrix sine-gordon equation. Conference Publications, 2009, 2009 (Special) : 678-690. doi: 10.3934/proc.2009.2009.678
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