Rational solitons for non-local Hirota equations: Robustness and cascading instability
The Hirota equation is a higher-order non-linear Schrödinger equation by incorporating third-order dispersion. Two pairs of non-local Hirota equations are studied. One is a parity transformed conjugate pair, and the other is a conjugate PT-symmetric pair. For the first pair, rational solitons are de...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-02-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1091526/full |
| _version_ | 1811170396220686336 |
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| author | Q. Pan H. M. Yin K. W. Chow |
| author_facet | Q. Pan H. M. Yin K. W. Chow |
| author_sort | Q. Pan |
| collection | DOAJ |
| description | The Hirota equation is a higher-order non-linear Schrödinger equation by incorporating third-order dispersion. Two pairs of non-local Hirota equations are studied. One is a parity transformed conjugate pair, and the other is a conjugate PT-symmetric pair. For the first pair, rational solitons are derived by the Darboux transformation, and are shown computationally to exhibit robust propagation properties. These rational solitons can exhibit both elastic and inelastic interactions. One particular case of an elastic collision between dark and “anti-dark” solitons is demonstrated. For the second pair, a “cascading mechanism” illustrating the growth of higher-order sidebands is elucidated explicitly for these non-local, conjugate PT-symmetric equations. These mechanisms provide a theoretical confirmation of the initial amplification phase of the growth-and-decay cycles of breathers. Such repeated patterns will serve as a manifestation of the classical Fermi-Pasta-Ulam-Tsingou recurrence. |
| first_indexed | 2024-04-10T16:56:04Z |
| format | Article |
| id | doaj.art-22eb994487744ba8ba0074ee536be2bf |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-10T16:56:04Z |
| publishDate | 2023-02-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-22eb994487744ba8ba0074ee536be2bf2023-02-07T06:55:55ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-02-011110.3389/fphy.2023.10915261091526Rational solitons for non-local Hirota equations: Robustness and cascading instabilityQ. PanH. M. YinK. W. ChowThe Hirota equation is a higher-order non-linear Schrödinger equation by incorporating third-order dispersion. Two pairs of non-local Hirota equations are studied. One is a parity transformed conjugate pair, and the other is a conjugate PT-symmetric pair. For the first pair, rational solitons are derived by the Darboux transformation, and are shown computationally to exhibit robust propagation properties. These rational solitons can exhibit both elastic and inelastic interactions. One particular case of an elastic collision between dark and “anti-dark” solitons is demonstrated. For the second pair, a “cascading mechanism” illustrating the growth of higher-order sidebands is elucidated explicitly for these non-local, conjugate PT-symmetric equations. These mechanisms provide a theoretical confirmation of the initial amplification phase of the growth-and-decay cycles of breathers. Such repeated patterns will serve as a manifestation of the classical Fermi-Pasta-Ulam-Tsingou recurrence.https://www.frontiersin.org/articles/10.3389/fphy.2023.1091526/fullrational solitonselastic and inelastic interactionsnon-local Hirota equationsrobustness testcascading instability |
| spellingShingle | Q. Pan H. M. Yin K. W. Chow Rational solitons for non-local Hirota equations: Robustness and cascading instability Frontiers in Physics rational solitons elastic and inelastic interactions non-local Hirota equations robustness test cascading instability |
| title | Rational solitons for non-local Hirota equations: Robustness and cascading instability |
| title_full | Rational solitons for non-local Hirota equations: Robustness and cascading instability |
| title_fullStr | Rational solitons for non-local Hirota equations: Robustness and cascading instability |
| title_full_unstemmed | Rational solitons for non-local Hirota equations: Robustness and cascading instability |
| title_short | Rational solitons for non-local Hirota equations: Robustness and cascading instability |
| title_sort | rational solitons for non local hirota equations robustness and cascading instability |
| topic | rational solitons elastic and inelastic interactions non-local Hirota equations robustness test cascading instability |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1091526/full |
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