Integrable ordinary differential equations on free associative algebras
We consider a classification problem for integrable nonlinear ordinary differential equations with an independent variable belonging to a free associative algebra M. Every equation of this type admits an m×m matrix reduction for an arbitrary m. The existence of symmetries or first integrals belonging to M is used as an integrability criterion.
KeywordsLocal Operator Hamiltonian Operator Recursion Operator Undetermined Coefficient Free Associative Algebra
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