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arXiv · 2503.12740

Pfaffian solution for dark-dark soliton to the coupled complex modified Korteweg-de Vries equation

Chenxi Li·Xiaochuan Liu·Bao-Feng Feng
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Abstract

In this paper, we study coupled complex modified Korteweg-de Vries (ccmKdV) equation by combining the Hirota's method and the Kadomtsev-Petviashvili (KP) reduction method. First, we show that the bilinear form of the ccmKdV equation under nonzero boundary condition is linked to the discrete BKP hierarchy through Miwa transformation. Based on this finding, we construct the dark-dark soliton solution in the pfaffian form. The dynamical behaviors for one- and two-soliton are analyzed and illustrated.

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Chenxi Li, Xiaochuan Liu, Bao-Feng Feng. 2025-03-17. Pfaffian solution for dark-dark soliton to the coupled complex modified Korteweg-de Vries equation. https://arxiv.org/abs/2503.12740

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