Coherent structure of Alice-Bob modified Korteweg de-Vries Equation
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866913371985543168 |
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| author | Li, Congcong Lou, S. Y. Jia, Man |
| author_facet | Li, Congcong Lou, S. Y. Jia, Man |
| contents | To describe two-place events, Alice-Bob systems have been established by means of the shifted parity and delayed time reversal in Ref. [1]. In this paper, we mainly study exact solutions of the integrable Alice-Bob modified Korteweg de-Vries (AB-mKdV) system. The general Nth Darboux transformation for the AB-mKdV equation are constructed. By using the Darboux transformation, some types of shifted parity and time reversal symmetry breaking solutions including one-soliton, two-soliton and rogue wave solutions are explicitly obtained. In addition to the similar solutions of the mKdV equation (group invariant solutions), there are abundant new localized structures for the AB-mKdV systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1706_08178 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Coherent structure of Alice-Bob modified Korteweg de-Vries Equation Li, Congcong Lou, S. Y. Jia, Man Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons To describe two-place events, Alice-Bob systems have been established by means of the shifted parity and delayed time reversal in Ref. [1]. In this paper, we mainly study exact solutions of the integrable Alice-Bob modified Korteweg de-Vries (AB-mKdV) system. The general Nth Darboux transformation for the AB-mKdV equation are constructed. By using the Darboux transformation, some types of shifted parity and time reversal symmetry breaking solutions including one-soliton, two-soliton and rogue wave solutions are explicitly obtained. In addition to the similar solutions of the mKdV equation (group invariant solutions), there are abundant new localized structures for the AB-mKdV systems. |
| title | Coherent structure of Alice-Bob modified Korteweg de-Vries Equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/1706.08178 |