Stochastic Analysis and White Noise Calculus of Nonlinear Wave Equations with Application to Laser Propagation and Generation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913622417997824 |
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| author | Sritharan, Sivaguru S. Mudaliar, Saba |
| author_facet | Sritharan, Sivaguru S. Mudaliar, Saba |
| contents | In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models, free electron laser generation models, as well as laser-plasma interaction models have been cast in a convenient and unified abstract framework as semilinear evolution equations in a Hilbert space to enable stochastic analysis. We formulate Ito calculus and white noise calculus methods of treating stochastic terms and prove existence and uniqueness of mild solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_16013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Analysis and White Noise Calculus of Nonlinear Wave Equations with Application to Laser Propagation and Generation Sritharan, Sivaguru S. Mudaliar, Saba Analysis of PDEs Mathematical Physics Functional Analysis Probability Quantum Algebra 81S20, 81V10, 60G51, 60H15, 60H17 In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models, free electron laser generation models, as well as laser-plasma interaction models have been cast in a convenient and unified abstract framework as semilinear evolution equations in a Hilbert space to enable stochastic analysis. We formulate Ito calculus and white noise calculus methods of treating stochastic terms and prove existence and uniqueness of mild solutions. |
| title | Stochastic Analysis and White Noise Calculus of Nonlinear Wave Equations with Application to Laser Propagation and Generation |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Probability Quantum Algebra 81S20, 81V10, 60G51, 60H15, 60H17 |
| url | https://arxiv.org/abs/2411.16013 |