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.

14 pages; 4 pictures

References in corpus (4)

• On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
• Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
• Noncommutative Solitons and D-branes
• Subvarieties in non-compact hyperkaehler manifolds

Cited by in corpus (13)

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