Mahmoud A E Abdelrahman, M A Sohaly, Yousef F Alharbi
{"title":"A new structure of stochastic solutions to the NLSE in unstable dispersive environments via Rayleigh distribution","authors":"Mahmoud A E Abdelrahman, M A Sohaly, Yousef F Alharbi","doi":"10.1007/s12043-023-02591-4","DOIUrl":null,"url":null,"abstract":"<div><p>The unstable nonlinear Schrödinger equation (UNLSE) characterises the time evolution of disturbances through unstable or marginally stable media. We study the stochastic UNLSE and stochastic modified UNLSE (mUNLSE). We apply the unified solver to provide some new stochastic solutions via Rayleigh distribution. The gained stochastic solutions play a crucial role in nonlinear sciences. Rayleigh distribution is used to depict the dispersion random input. In light of description of the behaviour of stochastic solutions, their mean and variance are illustrated. We show the influence of random parameters on the gained stochastic solutions. With the aid of Maple software, various profile pictures are introduced to exhibit the dynamical behaviour of the stochastic solutions.\n</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"97 3","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s12043-023-02591-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The unstable nonlinear Schrödinger equation (UNLSE) characterises the time evolution of disturbances through unstable or marginally stable media. We study the stochastic UNLSE and stochastic modified UNLSE (mUNLSE). We apply the unified solver to provide some new stochastic solutions via Rayleigh distribution. The gained stochastic solutions play a crucial role in nonlinear sciences. Rayleigh distribution is used to depict the dispersion random input. In light of description of the behaviour of stochastic solutions, their mean and variance are illustrated. We show the influence of random parameters on the gained stochastic solutions. With the aid of Maple software, various profile pictures are introduced to exhibit the dynamical behaviour of the stochastic solutions.
期刊介绍：
Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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