{"title":"摄动KDV和耗散NLS方程的近似波解:加权残差法","authors":"H. Demiray","doi":"10.26837/JAEM.590449","DOIUrl":null,"url":null,"abstract":"In the present work, we modified the conventional ”weighted residual method” to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative effects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"AN APPROXIMATE WAVE SOLUTION FOR PERTURBED KDV AND DISSIPATIVE NLS EQUATIONS: WEIGHTED RESIDUAL METHOD\",\"authors\":\"H. Demiray\",\"doi\":\"10.26837/JAEM.590449\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present work, we modified the conventional ”weighted residual method” to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative effects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.\",\"PeriodicalId\":44094,\"journal\":{\"name\":\"TWMS Journal of Applied and Engineering Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"TWMS Journal of Applied and Engineering Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26837/JAEM.590449\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"TWMS Journal of Applied and Engineering Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26837/JAEM.590449","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
AN APPROXIMATE WAVE SOLUTION FOR PERTURBED KDV AND DISSIPATIVE NLS EQUATIONS: WEIGHTED RESIDUAL METHOD
In the present work, we modified the conventional ”weighted residual method” to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative effects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.
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