Noncommutative AKNS systems and multisolitonsolutions to the matrix sine-gordon equation

Cornelia Schiebold

doi:10.3934/proc.2009.2009.678

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2009, Volume 2009: 678-690. Doi: 10.3934/proc.2009.2009.678 open access

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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

Received: May 31, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q51, 47J25, 35C05; Secondary: 35Q53, 35Q55.

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