Oscillatory solitons of U(1)-invariant mKdV equations I: Envelope speed and temporal frequency
| Autor: | Anco, Stephen C., Mia, Abdus Sattar, Willoughby, Mark R. |
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| Rok vydání: | 2014 |
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| Zdroj: | J. Math. Phys. 56 (2015) 101506 (35 pages) |
| Druh dokumentu: | Working Paper |
| Popis: | Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation, given by the Hirota equation and the Sasa-Satsuma equation. A bilinear formulation of these two equations is used to derive the oscillatory 1-soliton and 2-soliton solutions, which are then written out in a physical form parameterized in terms of their speed, modulation frequency, and phase. Depending on the modulation frequency, the speeds of oscillatory waves (1-solitons) can be positive, negative, or zero, in contrast to the strictly positive speed of ordinary solitons. When the speed is zero, an oscillatory wave is a time-periodic standing wave. Properties of the amplitude and phase of oscillatory 1-solitons are derived. Oscillatory 2-solitons are graphically illustrated to describe collisions between two oscillatory 1-solitons in the case when the speeds are distinct. In the special case of equal speeds, oscillatory 2-solitons are shown to reduce to harmonically modulated breather waves. Comment: 47 pages, 24 figures |
| Databáze: | arXiv |
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