Dynamics from a mathematical model of a two-state gas laser
Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations....
| Main Authors: | , , , , |
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| Format: | Journal article |
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Elsevier
2018
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| _version_ | 1797056924960686080 |
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| author | Kleanthous, A Hua, T Manai, A Yawar, K Van Gorder, R |
| author_facet | Kleanthous, A Hua, T Manai, A Yawar, K Van Gorder, R |
| author_sort | Kleanthous, A |
| collection | OXFORD |
| description | Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger’s equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger’s equation, with no evidence of shock formation or loss of regularity. |
| first_indexed | 2024-03-06T19:29:21Z |
| format | Journal article |
| id | oxford-uuid:1ce8e0c1-8b99-44c7-bc27-dccd52095a01 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:29:21Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:1ce8e0c1-8b99-44c7-bc27-dccd52095a012022-03-26T11:08:06ZDynamics from a mathematical model of a two-state gas laserJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1ce8e0c1-8b99-44c7-bc27-dccd52095a01Symplectic Elements at OxfordElsevier2018Kleanthous, AHua, TManai, AYawar, KVan Gorder, RMotivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger’s equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger’s equation, with no evidence of shock formation or loss of regularity. |
| spellingShingle | Kleanthous, A Hua, T Manai, A Yawar, K Van Gorder, R Dynamics from a mathematical model of a two-state gas laser |
| title | Dynamics from a mathematical model of a two-state gas laser |
| title_full | Dynamics from a mathematical model of a two-state gas laser |
| title_fullStr | Dynamics from a mathematical model of a two-state gas laser |
| title_full_unstemmed | Dynamics from a mathematical model of a two-state gas laser |
| title_short | Dynamics from a mathematical model of a two-state gas laser |
| title_sort | dynamics from a mathematical model of a two state gas laser |
| work_keys_str_mv | AT kleanthousa dynamicsfromamathematicalmodelofatwostategaslaser AT huat dynamicsfromamathematicalmodelofatwostategaslaser AT manaia dynamicsfromamathematicalmodelofatwostategaslaser AT yawark dynamicsfromamathematicalmodelofatwostategaslaser AT vangorderr dynamicsfromamathematicalmodelofatwostategaslaser |