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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.05548 |
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| _version_ | 1866916352892076032 |
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| author | Bonnemain, Thibault Doyon, Benjamin Biondini, Gino Roberti, Giacomo El, Gennady A. |
| author_facet | Bonnemain, Thibault Doyon, Benjamin Biondini, Gino Roberti, Giacomo El, Gennady A. |
| contents | We study two-dimensional stationary soliton gas in the framework of the time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which coincides with the integrable two-way ``good'' Boussinesq equation in the xy-plane. This (2+0)D reduction enables the construction of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalised hydrodynamics of the Boussinesq equation. We then use the kinetic theory to analytically describe two basic types of 2D soliton gas interactions: (i) refraction of a line soliton by a stationary soliton gas, and (ii) oblique interference of two soliton gases. We verify the analytical predictions by numerically implementing the corresponding KPII soliton gases via exact N-soliton solutions with N-large and appropriately chosen random distributions for the soliton parameters. We also explicitly evaluate the long-distance correlations for the two-component interference configurations. The results can be applied to a variety of physical systems, from shallow water waves to Bose-Einstein condensates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-dimensional stationary soliton gas Bonnemain, Thibault Doyon, Benjamin Biondini, Gino Roberti, Giacomo El, Gennady A. Pattern Formation and Solitons We study two-dimensional stationary soliton gas in the framework of the time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which coincides with the integrable two-way ``good'' Boussinesq equation in the xy-plane. This (2+0)D reduction enables the construction of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalised hydrodynamics of the Boussinesq equation. We then use the kinetic theory to analytically describe two basic types of 2D soliton gas interactions: (i) refraction of a line soliton by a stationary soliton gas, and (ii) oblique interference of two soliton gases. We verify the analytical predictions by numerically implementing the corresponding KPII soliton gases via exact N-soliton solutions with N-large and appropriately chosen random distributions for the soliton parameters. We also explicitly evaluate the long-distance correlations for the two-component interference configurations. The results can be applied to a variety of physical systems, from shallow water waves to Bose-Einstein condensates. |
| title | Two-dimensional stationary soliton gas |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2408.05548 |