Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation

Abstract

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of polarized kink solutions.

arXiv comment14 pages; 4 pictures

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• Noncommutative Solitons and Quasideterminants
• Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System
• Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations
• Dynamics of Rogue Waves in the Partially PT-symmetric Nonlocal Davey-Stewartson Systems
• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
• Bidifferential graded algebras and integrable systems
• Non-Abelian Toda lattice and analogs of Painlevé III equation
• Geometric algebra and quadrilateral lattices
• On soliton solutions of the time-discrete generalized lattice Heisenberg magnet model
• Solving non-abelian loop Toda equations
• Quasideterminant solutions to a noncommutative $q$-difference two-dimensional Toda lattice equation
• Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation
• 'Riemann Equations' in Bidifferential Calculus