非交换 KP 和 mKP 方程的扩展版本以及三浦变换

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-04-17 DOI:arxiv-2404.11391

Muhammad Kashif, Li Chunxia, Cui Mengyuan

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摘要

以统一的方式构建了非交换（nc）KP方程和nc mKP方程的扩展版本，并提出了两类准定解。在交换环境下，准定解分别为具有自洽源的双线性 KP 方程和具有自洽源的双线性 mKP 方程提供了已知和未知的 Wronskian 解和 Grammians 解。为扩展 nc KP 和 nc mKP 方程建立了 Miuratransformation。

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

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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arXiv - PHYS - Exactly Solvable and Integrable Systems

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