Lakhveer Kaur, Omer Mohammed Khodayer Al-Dulaimi, Farag Mahel Mohammed, Anwar Ja’afar Mohamad Jawad, Mohammad Abdelkawy, Oswaldo González-Gaxiola, Ahmed H. Arnous, Anjan Biswas
{"title":"离散三重态双层流体流动的孤立波和激波:Zaremaoghaddam和Gear-Grimshaw模型(KdV方程)","authors":"Lakhveer Kaur, Omer Mohammed Khodayer Al-Dulaimi, Farag Mahel Mohammed, Anwar Ja’afar Mohamad Jawad, Mohammad Abdelkawy, Oswaldo González-Gaxiola, Ahmed H. Arnous, Anjan Biswas","doi":"10.1186/s43088-025-00679-x","DOIUrl":null,"url":null,"abstract":"<div><h3>Background</h3><p>The Zaremaoghaddam model studies internal waves, fluid dynamics, and nonlinear wave equations. In shallow water, internal solitons, or stratified fluids, the procedure may involve modifying or applying nonlinear wave models like Korteweg–de Vries equation, Boussinesq, or Gear–Grimshaw. The Gear–Grimshaw system simulates internal waves in a two-layer stratified fluid, such as an ocean with two density layers, using interconnected nonlinear evolution equations. The Korteweg–de Vries equation is extended to include wave mode interactions.</p><h3>Results</h3><p>The paper recovers solitary waves and shock waves for double-layered fluid flow that is modeled whose basic platform is the Korteweg–de Vries equation. This retrieval is made possible with the usage of the generalized exponential differential rational function approach. Two models for the double-layered flow are taken into consideration, namely the Zaremaoghaddam model and the Gear–Grimshaw model. The parameter restrictions for the existence of such solutions are also enumerated.</p><h3>Conclusions</h3><p>This paper has many implications and opens up many future opportunities. Since double-layered fluid flow never addresses rogue wave features, the paper’s results would be the foundation for studying them. Additionally, viscosity can be considered in the two models in this paper. A practical perspective would result since viscosity is inevitable in any fluid or airflow. Additionally, these models are new. Thus, such models must be investigated by identifying conservation laws and studying soliton perturbation theory.</p></div>","PeriodicalId":481,"journal":{"name":"Beni-Suef University Journal of Basic and Applied Sciences","volume":"14 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://bjbas.springeropen.com/counter/pdf/10.1186/s43088-025-00679-x","citationCount":"0","resultStr":"{\"title\":\"Solitary waves and shock waves for double-layered fluid flow with dispersion triplet: Zaremaoghaddam and Gear–Grimshaw models (KdV equation)\",\"authors\":\"Lakhveer Kaur, Omer Mohammed Khodayer Al-Dulaimi, Farag Mahel Mohammed, Anwar Ja’afar Mohamad Jawad, Mohammad Abdelkawy, Oswaldo González-Gaxiola, Ahmed H. Arnous, Anjan Biswas\",\"doi\":\"10.1186/s43088-025-00679-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><h3>Background</h3><p>The Zaremaoghaddam model studies internal waves, fluid dynamics, and nonlinear wave equations. In shallow water, internal solitons, or stratified fluids, the procedure may involve modifying or applying nonlinear wave models like Korteweg–de Vries equation, Boussinesq, or Gear–Grimshaw. The Gear–Grimshaw system simulates internal waves in a two-layer stratified fluid, such as an ocean with two density layers, using interconnected nonlinear evolution equations. The Korteweg–de Vries equation is extended to include wave mode interactions.</p><h3>Results</h3><p>The paper recovers solitary waves and shock waves for double-layered fluid flow that is modeled whose basic platform is the Korteweg–de Vries equation. This retrieval is made possible with the usage of the generalized exponential differential rational function approach. Two models for the double-layered flow are taken into consideration, namely the Zaremaoghaddam model and the Gear–Grimshaw model. The parameter restrictions for the existence of such solutions are also enumerated.</p><h3>Conclusions</h3><p>This paper has many implications and opens up many future opportunities. Since double-layered fluid flow never addresses rogue wave features, the paper’s results would be the foundation for studying them. Additionally, viscosity can be considered in the two models in this paper. A practical perspective would result since viscosity is inevitable in any fluid or airflow. Additionally, these models are new. 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Solitary waves and shock waves for double-layered fluid flow with dispersion triplet: Zaremaoghaddam and Gear–Grimshaw models (KdV equation)
Background
The Zaremaoghaddam model studies internal waves, fluid dynamics, and nonlinear wave equations. In shallow water, internal solitons, or stratified fluids, the procedure may involve modifying or applying nonlinear wave models like Korteweg–de Vries equation, Boussinesq, or Gear–Grimshaw. The Gear–Grimshaw system simulates internal waves in a two-layer stratified fluid, such as an ocean with two density layers, using interconnected nonlinear evolution equations. The Korteweg–de Vries equation is extended to include wave mode interactions.
Results
The paper recovers solitary waves and shock waves for double-layered fluid flow that is modeled whose basic platform is the Korteweg–de Vries equation. This retrieval is made possible with the usage of the generalized exponential differential rational function approach. Two models for the double-layered flow are taken into consideration, namely the Zaremaoghaddam model and the Gear–Grimshaw model. The parameter restrictions for the existence of such solutions are also enumerated.
Conclusions
This paper has many implications and opens up many future opportunities. Since double-layered fluid flow never addresses rogue wave features, the paper’s results would be the foundation for studying them. Additionally, viscosity can be considered in the two models in this paper. A practical perspective would result since viscosity is inevitable in any fluid or airflow. Additionally, these models are new. Thus, such models must be investigated by identifying conservation laws and studying soliton perturbation theory.
期刊介绍:
Beni-Suef University Journal of Basic and Applied Sciences (BJBAS) is a peer-reviewed, open-access journal. This journal welcomes submissions of original research, literature reviews, and editorials in its respected fields of fundamental science, applied science (with a particular focus on the fields of applied nanotechnology and biotechnology), medical sciences, pharmaceutical sciences, and engineering. The multidisciplinary aspects of the journal encourage global collaboration between researchers in multiple fields and provide cross-disciplinary dissemination of findings.