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The extended versions of the noncommutative KP and mKP equations and Miura transformation

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arxiv 2404.11391 v1 pith:X4SB7PL2 submitted 2024-04-17 nlin.SI

Muhammad Kashif , Li Chunxia , Cui Mengyuan This is my paper · ORCID
classification nlin.SI
keywords equationextendedsolutionsbilinearequationsmiuranoncommutativequasideterminant
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Extended versions of the noncommutative(nc) KP equation and the nc mKP equation are constructed in a unified way, for which two types of quasideterminant solutions are also presented. In commutative setting, the quasideterminant solutions provide the known and unknown Wronskian and Grammian solutions for the bilinear KP equation with self-consistent sources and the bilinear mKP equation with self-consistent sources, respectively. Miura transformation is established for the extended nc KP and nc mKP equations.

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  1. Quasi-Pfaffian Solutions to Integrable Systems via Sylvester-Moutard Transformations

    math-ph 2026-07 conditional novelty 4.0 of 10

    The quasi-Pfaffian reformulation of the Moutard transform reproduces the known Moutard solution class for integrable equations and leaves a noncommutative generalization unproved.

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