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

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Main Authors: Sun, Hong-Qian, Shen, Shou-Feng, Zhu, Zuo-Nong
Format: Preprint
Published: 2025
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author Sun, Hong-Qian
Shen, Shou-Feng
Zhu, Zuo-Nong
author_facet Sun, Hong-Qian
Shen, Shou-Feng
Zhu, Zuo-Nong
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_13647
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A nonlocal coupled modified complex integrable dispersionless equation: Darboux transformation, soliton-type solutions and its asymptotic behavior
Sun, Hong-Qian
Shen, Shou-Feng
Zhu, Zuo-Nong
Exactly Solvable and Integrable Systems
35Q51, 37K10, 37K15
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.
title A nonlocal coupled modified complex integrable dispersionless equation: Darboux transformation, soliton-type solutions and its asymptotic behavior
topic Exactly Solvable and Integrable Systems
35Q51, 37K10, 37K15
url https://arxiv.org/abs/2510.13647