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