Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems
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arXiv
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| Natura: | Preprint |
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2018
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| _version_ | 1866910465899102208 |
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| author | Lou, S. Y. |
| author_facet | Lou, S. Y. |
| contents | It is found that two different celebrate models, the Korteweg de-Vrise (KdV) equation and the Boussinesq equation, are linked to a same model equation but with different nonlocalities. The model equation is called the Alice-Bob KdV (ABKdV) equation which was derived from the usual KdV equation via the so-called consistent correlated bang (CCB) companied by the shifted parity (SP) and delayed time reversal (DTR). The same model can be called as the Alice-Bob Boussinesq (ABB) system if the nonlocality is changed as only one of SP and DTR. For the ABB systems, with help of the bilinear approach and recasting the multi-soliton solutions of the usual Boussinesq equation to an equivalent novel form, the multi-soliton solutions with even numbers and the head on interactions are obtained. However, the multi-soliton solutions with odd numbers and the multi-soliton solutions with even numbers but with pursuant interactions are prohibited. For the ABKdV equation, the multi-soliton solutions exhibit many more structures because an arbitrary odd function of $x+t$ can be introduced as background waves of the usual KdV equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_07559 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems Lou, S. Y. Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons It is found that two different celebrate models, the Korteweg de-Vrise (KdV) equation and the Boussinesq equation, are linked to a same model equation but with different nonlocalities. The model equation is called the Alice-Bob KdV (ABKdV) equation which was derived from the usual KdV equation via the so-called consistent correlated bang (CCB) companied by the shifted parity (SP) and delayed time reversal (DTR). The same model can be called as the Alice-Bob Boussinesq (ABB) system if the nonlocality is changed as only one of SP and DTR. For the ABB systems, with help of the bilinear approach and recasting the multi-soliton solutions of the usual Boussinesq equation to an equivalent novel form, the multi-soliton solutions with even numbers and the head on interactions are obtained. However, the multi-soliton solutions with odd numbers and the multi-soliton solutions with even numbers but with pursuant interactions are prohibited. For the ABKdV equation, the multi-soliton solutions exhibit many more structures because an arbitrary odd function of $x+t$ can be introduced as background waves of the usual KdV equation. |
| title | Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/1806.07559 |