A novel noncommutative KdV-type equation, its recursion operator, and solitons
arXiv:1704.03208 · doi:10.1063/1.5027481
Abstract
A noncommutative KdV-type equation is introduced extending the Baecklund chart in [S. Carillo, M. Lo Schiavo, and C. Schiebold, SIGMA 12 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in [P.J. Olver and V.V. Sokolov Commun. Math. Phys. 193 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies and an explicit solution class are derived.
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Cited by in corpus (7)
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- The Gross-Pitaevskii equation: Bäcklund transformations and admitted solutions
- Soliton equations: admitted solutions and invariances via Bäcklund transformations
- Differential substitutions for non-Abelian equations of KdV type
- Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions