{"title":"非线性薛定谔型分数阶偏微分方程的波结构在物理科学中出现","authors":"Mst. Nasrin Nahar, M. Islam, Diganta Broto Kar","doi":"10.18034/EI.V9I2.560","DOIUrl":null,"url":null,"abstract":"Nonlinear partial differential equations are mostly renowned for depicting the underlying behavior of nonlinear phenomena relating to the nature of the real world. In this paper, we discuss analytic solutions of fractional-order nonlinear Schrodinger types equations such as the space-time fractional nonlinear Schrodinger equation and the (2+1)-dimensional time-fractional Schrodinger equation. The considered equations are converted into ordinary differential equations with the help of wave variable transformation and then the recently established rational ( )-expansion method is employed to construct the exact solutions. The obtained solutions have appeared in the forms of a trigonometric function, hyperbolic function, and rational function which are compared with those of literature and claimed to be different. The graphical representations of the solutions are finally brought out for their physical appearances. The applied method is seemed to be efficient, concise, and productive which might be used for further research. \nMathematics Subject Classifications: 35C08, 35R11","PeriodicalId":49736,"journal":{"name":"Nuclear Engineering International","volume":"31 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wave Structures for Nonlinear Schrodinger Types Fractional Partial Differential Equations Arise in Physical Sciences\",\"authors\":\"Mst. Nasrin Nahar, M. Islam, Diganta Broto Kar\",\"doi\":\"10.18034/EI.V9I2.560\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Nonlinear partial differential equations are mostly renowned for depicting the underlying behavior of nonlinear phenomena relating to the nature of the real world. In this paper, we discuss analytic solutions of fractional-order nonlinear Schrodinger types equations such as the space-time fractional nonlinear Schrodinger equation and the (2+1)-dimensional time-fractional Schrodinger equation. The considered equations are converted into ordinary differential equations with the help of wave variable transformation and then the recently established rational ( )-expansion method is employed to construct the exact solutions. The obtained solutions have appeared in the forms of a trigonometric function, hyperbolic function, and rational function which are compared with those of literature and claimed to be different. The graphical representations of the solutions are finally brought out for their physical appearances. The applied method is seemed to be efficient, concise, and productive which might be used for further research. \\nMathematics Subject Classifications: 35C08, 35R11\",\"PeriodicalId\":49736,\"journal\":{\"name\":\"Nuclear Engineering International\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nuclear Engineering International\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.18034/EI.V9I2.560\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Engineering International","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.18034/EI.V9I2.560","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Engineering","Score":null,"Total":0}
Wave Structures for Nonlinear Schrodinger Types Fractional Partial Differential Equations Arise in Physical Sciences
Nonlinear partial differential equations are mostly renowned for depicting the underlying behavior of nonlinear phenomena relating to the nature of the real world. In this paper, we discuss analytic solutions of fractional-order nonlinear Schrodinger types equations such as the space-time fractional nonlinear Schrodinger equation and the (2+1)-dimensional time-fractional Schrodinger equation. The considered equations are converted into ordinary differential equations with the help of wave variable transformation and then the recently established rational ( )-expansion method is employed to construct the exact solutions. The obtained solutions have appeared in the forms of a trigonometric function, hyperbolic function, and rational function which are compared with those of literature and claimed to be different. The graphical representations of the solutions are finally brought out for their physical appearances. The applied method is seemed to be efficient, concise, and productive which might be used for further research.
Mathematics Subject Classifications: 35C08, 35R11