Two-dimensional stationary soliton gas
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 spatial anal...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013143 |
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| author | Thibault Bonnemain Gino Biondini Benjamin Doyon Giacomo Roberti Gennady A. El |
| author_facet | Thibault Bonnemain Gino Biondini Benjamin Doyon Giacomo Roberti Gennady A. El |
| author_sort | Thibault Bonnemain |
| collection | DOAJ |
| description | 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 spatial analog of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalized hydrodynamics of the Boussinesq equation. We then use the spectral 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 | Article |
| id | doaj-art-cc76b23b14cd49c58b0957f69cc37f4f |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-cc76b23b14cd49c58b0957f69cc37f4f2025-02-07T15:18:24ZengAmerican Physical SocietyPhysical Review Research2643-15642025-02-017101314310.1103/PhysRevResearch.7.013143Two-dimensional stationary soliton gasThibault BonnemainGino BiondiniBenjamin DoyonGiacomo RobertiGennady A. ElWe 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 spatial analog of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalized hydrodynamics of the Boussinesq equation. We then use the spectral 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.http://doi.org/10.1103/PhysRevResearch.7.013143 |
| spellingShingle | Thibault Bonnemain Gino Biondini Benjamin Doyon Giacomo Roberti Gennady A. El Two-dimensional stationary soliton gas Physical Review Research |
| title | Two-dimensional stationary soliton gas |
| title_full | Two-dimensional stationary soliton gas |
| title_fullStr | Two-dimensional stationary soliton gas |
| title_full_unstemmed | Two-dimensional stationary soliton gas |
| title_short | Two-dimensional stationary soliton gas |
| title_sort | two dimensional stationary soliton gas |
| url | http://doi.org/10.1103/PhysRevResearch.7.013143 |
| work_keys_str_mv | AT thibaultbonnemain twodimensionalstationarysolitongas AT ginobiondini twodimensionalstationarysolitongas AT benjamindoyon twodimensionalstationarysolitongas AT giacomoroberti twodimensionalstationarysolitongas AT gennadyael twodimensionalstationarysolitongas |