{"title":"Modeling of Physical Processes","authors":"B. Vick","doi":"10.21236/ada384825","DOIUrl":"https://doi.org/10.21236/ada384825","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87391404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical Solutions of Ordinary Differential Equations","authors":"B. Vick","doi":"10.1201/9781003002260-9","DOIUrl":"https://doi.org/10.1201/9781003002260-9","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78575727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introduction to Ordinary Differential Equations","authors":"B. Vick","doi":"10.1201/9781003002260-7","DOIUrl":"https://doi.org/10.1201/9781003002260-7","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81317361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear Algebra","authors":"B. Vick","doi":"10.1201/9781003002260-5","DOIUrl":"https://doi.org/10.1201/9781003002260-5","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82656728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Calculus","authors":"Brian Vick","doi":"10.1201/9781003002260-4","DOIUrl":"https://doi.org/10.1201/9781003002260-4","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90794393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this study, we consider the nonlinear propagation of shear horizontal (SH) waves in a layer of finite thickness. The materials of the layer are assumed to be heterogeneous, isotropic, and generalized neo-Hookean. We assume that heterogeneity varies only with the thickness and we choose hyperbolic functions for heterogeneity type. We also assume that the traction is free on the upper surface of the layer. Furthermore, the lower boundary is rigidly fixed. Using a perturbation method and keeping the balance of the nonlinearity and the dispersion in the analysis, we show that the self-modulation of nonlinear SH waves can be given by the nonlinear Schr¨odinger (NLS) equation. Using well known solutions of NLS equation, we find that the dark solitary SH waves can exist depending on the nonlinear constitution of the layer. Consequently, the effects of the heterogeneity and the nonlinearity on the deformation field are considered for these waves.
{"title":"NONLINEAR DARK SOLITARY SH WAVES IN A HETEROGENEOUS LAYER","authors":"D. Demirkuş","doi":"10.26837/jaem.627563","DOIUrl":"https://doi.org/10.26837/jaem.627563","url":null,"abstract":". In this study, we consider the nonlinear propagation of shear horizontal (SH) waves in a layer of finite thickness. The materials of the layer are assumed to be heterogeneous, isotropic, and generalized neo-Hookean. We assume that heterogeneity varies only with the thickness and we choose hyperbolic functions for heterogeneity type. We also assume that the traction is free on the upper surface of the layer. Furthermore, the lower boundary is rigidly fixed. Using a perturbation method and keeping the balance of the nonlinearity and the dispersion in the analysis, we show that the self-modulation of nonlinear SH waves can be given by the nonlinear Schr¨odinger (NLS) equation. Using well known solutions of NLS equation, we find that the dark solitary SH waves can exist depending on the nonlinear constitution of the layer. Consequently, the effects of the heterogeneity and the nonlinearity on the deformation field are considered for these waves.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46067875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"CONTINUOUS K-G-FUSION FRAMES IN HILBERT SPACES","authors":"E. Alizadeh, Asghar Rahim, E. Osgooei","doi":"10.26837/JAEM.606439","DOIUrl":"https://doi.org/10.26837/JAEM.606439","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41308343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ESTIMATION OF THE LOCATION AND SCALE PARAMETERS OF MOYAL DISTRIBUTION","authors":"T. Arslan, S. Acitas, B. Şenoğlu","doi":"10.26837/JAEM.590766","DOIUrl":"https://doi.org/10.26837/JAEM.590766","url":null,"abstract":"","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45596034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"AN APPROXIMATE WAVE SOLUTION FOR PERTURBED KDV AND DISSIPATIVE NLS EQUATIONS: WEIGHTED RESIDUAL METHOD","authors":"H. Demiray","doi":"10.26837/JAEM.590449","DOIUrl":"https://doi.org/10.26837/JAEM.590449","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":0.4,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43811803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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