A nonlocal coupled modified complex integrable dispersionless equation: Darboux transformation, soliton-type solutions and its asymptotic behavior

Hong-Qian Sun; Shou-Feng Shen; Zuo-Nong Zhu

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arXiv · 2510.13647

A nonlocal coupled modified complex integrable dispersionless equation: Darboux transformation, soliton-type solutions and its asymptotic behavior

Hong-Qian Sun·Shou-Feng Shen·Zuo-Nong Zhu

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Abstract

In this paper, we primarily construct Darboux transformation(DT) of the nonlocal coupled modified complex integrable dispersionless (cm-CID) equation, which is first proposed by the connection with a nonlocal coupled modified complex short pulse(cm-CSP) equation. Utilizing DT, we present soliton-type solutions for the nonlocal cm-CID equation under vanishing and non-vanishing boundary conditions. Soliton-type solutions include periodic wave, growing-, decaying-periodic wave, periodic-like wave (which consists of a mixture of periodic wave and breather wave, a combination of periodic wave and background plane), breather-like wave and rational solution. Furthermore, we have also analyzed asymptotic behavior and properties of these solutions theoretically and graphically. We must emphasis that soliton solutions of the nonlocal cm-CID equation possess novel properties that are distinct from those of the cm-CID equation, such as the nonlocal cm-CID equation has the growing-, decaying-periodic solution and periodic-like solution. The implications of these findings could potentially contribute to the description of optical pulse behavior during propagation in optical fibers.

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Hong-Qian Sun, Shou-Feng Shen, Zuo-Nong Zhu. 2025-10-15. A nonlocal coupled modified complex integrable dispersionless equation: Darboux transformation, soliton-type solutions and its asymptotic behavior. https://arxiv.org/abs/2510.13647

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