Construction of Type-II Backlund Transformation for the mKdV Hierarchy

Abstract

From an algebraic construction of the mKdV hierarchy we observe that the space component of the Lax operator play a role of an universal algebraic object. This fact induces the universality of a gauge transformation that relates two field configurations of a given member of the hierarchy. Such gauge transformation generates the Backlund transformation (BT). In this paper we propose a systematic construction of Backlund Transformation for the entire mKdV hierarchy form the known Type-II BT of the sinh-Gordon theory. We explicitly construct the BT of the first few integrable models associated to positive and negative grade-time evolutions. Solutions of these transformations for several cases describing the transition from vacuum-vacuum and the vacuum to one-soliton solutions which determines the value for the auxiliary field and the the Backlund parameter respectively, independently of the model. The same follows for the scattering of two one-soliton solutions. The resultant delay is determined by a condition independent of the model considered.

latex 21 pages

References in corpus (3)

• Type-II Bäcklund Transformations via Gauge Transformations
• Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model
• Backlund Transformation for Integrable Hierarchies: example - mKdV Hierarchy

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• Twisted Affine Integrable Hierarchies and Soliton Solutions
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• Recursion Operator and Bäcklund Transformation for Super mKdV Hierarchy