{"title":"Optical solutions to the truncated M-fractional Schrödinger–KdV equation via an analytical method","authors":"","doi":"10.1007/s10910-023-01554-9","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we will use the exp<span> <span>\\((-\\Phi (\\eta ))\\)</span> </span>-expansion method to obtain the solitonic wave solution in the sense of the truncated M-fractional Schrödinger–KdV equation. The provided equation is converted into an ordinary differential equation using the appropriate wave transformation. Standard waveform shapes are determined, such as hyperbolic, exponential, dark, bright, rational, plane, and combo bright-dark soliton. We create 2D, density, and contour graphs of the solutions using consistent parametric values to examine the physical characteristics of the constructed solitons. Using Wolfram Mathematica, the newly created solutions are verified by inserting them back into the model under consideration. The suggested method and results can also be used to analyze high-order fractional models found in fields such as optics, hydrodynamics, plasma, wave theory, and others.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1007/s10910-023-01554-9","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we will use the exp\((-\Phi (\eta ))\)-expansion method to obtain the solitonic wave solution in the sense of the truncated M-fractional Schrödinger–KdV equation. The provided equation is converted into an ordinary differential equation using the appropriate wave transformation. Standard waveform shapes are determined, such as hyperbolic, exponential, dark, bright, rational, plane, and combo bright-dark soliton. We create 2D, density, and contour graphs of the solutions using consistent parametric values to examine the physical characteristics of the constructed solitons. Using Wolfram Mathematica, the newly created solutions are verified by inserting them back into the model under consideration. The suggested method and results can also be used to analyze high-order fractional models found in fields such as optics, hydrodynamics, plasma, wave theory, and others.
期刊介绍:
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.