{"title":"Solitary Waves of 1-Nonlinear Schrödinger Equation in the Composite Right- and Left-Handed Metamaterial","authors":"A. Sci","doi":"10.4208/jpde.v32.n4.1","DOIUrl":null,"url":null,"abstract":"In this article, we analyze solitary waves in nonlinear left-handed transmission line with nonlinear diodes (Schottkys) which is an important issue, especially for soliton devices. By applying the Kirchhoffs laws and reductive direct method, the voltage in the spectral domain was obtained. Considering the Taylor series around a certain modulation frequency, we obtained one dimensional Nonlinear Schrödinger Equation (NSE), which support envelops soliton, and bright soliton solutions. Using sine-cosine mathematical method, soliton solutions of the standard Nonlinear Schröd-inger equation are obtained. The method used is straightforward and concise and can be applied to solve further of nonlinear PDEs in mathematical physics. AMS Subject Classifications: 060.2310, 35G20, 34G20 Chinese Library Classifications: O175.29","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jpde.v32.n4.1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we analyze solitary waves in nonlinear left-handed transmission line with nonlinear diodes (Schottkys) which is an important issue, especially for soliton devices. By applying the Kirchhoffs laws and reductive direct method, the voltage in the spectral domain was obtained. Considering the Taylor series around a certain modulation frequency, we obtained one dimensional Nonlinear Schrödinger Equation (NSE), which support envelops soliton, and bright soliton solutions. Using sine-cosine mathematical method, soliton solutions of the standard Nonlinear Schröd-inger equation are obtained. The method used is straightforward and concise and can be applied to solve further of nonlinear PDEs in mathematical physics. AMS Subject Classifications: 060.2310, 35G20, 34G20 Chinese Library Classifications: O175.29
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