{"title":"分数阶广义等宽- burgers模型的波前动力结构的两种解析格式:参数和分数阶的影响","authors":"Mst. Razia Pervin, Harun-Or- Roshid, Alrazi Abdeljabbar, Pinakee Dey, Shewli Shamim Shanta","doi":"10.1515/nleng-2022-0328","DOIUrl":null,"url":null,"abstract":"Abstract This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":"20 1","pages":"0"},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Dynamical structures of wave front to the fractional generalized equal width-Burgers model <i>via</i> two analytic schemes: Effects of parameters and fractionality\",\"authors\":\"Mst. Razia Pervin, Harun-Or- Roshid, Alrazi Abdeljabbar, Pinakee Dey, Shewli Shamim Shanta\",\"doi\":\"10.1515/nleng-2022-0328\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.\",\"PeriodicalId\":37863,\"journal\":{\"name\":\"Nonlinear Engineering - Modeling and Application\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Engineering - Modeling and Application\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/nleng-2022-0328\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0328","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Dynamical structures of wave front to the fractional generalized equal width-Burgers model via two analytic schemes: Effects of parameters and fractionality
Abstract This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.
期刊介绍:
The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.