A noncommutative semi-discrete Toda equation and its quasideterminant solutions
C.X. Li, J.J.C. Nimmo
TL;DR
This paper introduces a noncommutative semi-discrete Toda equation, develops its Lax pair and Darboux transformations, and constructs quasideterminant solutions, advancing the understanding of integrable systems in noncommutative settings.
Contribution
It presents the first formulation of a noncommutative semi-discrete Toda equation along with explicit quasideterminant solutions, expanding integrable systems theory.
Findings
Derived Lax pair for the noncommutative semi-discrete Toda equation
Constructed Darboux and binary Darboux transformations
Produced quasideterminant solutions for the equation
Abstract
A noncommutative version of the semi-discrete Toda equation is considered. A Lax pair and its Darboux transformations and binary Darboux transformations are found and they are used to construct two families of quasideterminant solutions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Topics in Algebra