Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866909128829435904 |
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| author | Modak, Subhrajit Singh, Akhil P. Panigrahi, P. K. |
| author_facet | Modak, Subhrajit Singh, Akhil P. Panigrahi, P. K. |
| contents | We demonstrate the existence of complex solitary wave and periodic solutions of the Kortweg de-vries (KdV) and modified Kortweg de-Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity ($\cal{P}$) and time-reversal ($\cal{T}$) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The $\cal{PT}$-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental $sech^2$ solution through supersymmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1509_01712 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations Modak, Subhrajit Singh, Akhil P. Panigrahi, P. K. Mathematical Physics Pattern Formation and Solitons We demonstrate the existence of complex solitary wave and periodic solutions of the Kortweg de-vries (KdV) and modified Kortweg de-Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity ($\cal{P}$) and time-reversal ($\cal{T}$) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The $\cal{PT}$-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental $sech^2$ solution through supersymmetry. |
| title | Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations |
| topic | Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/1509.01712 |