{"title":"Bäcklund Transformations of the Relativistic Schrödinger Equation","authors":"M. V. Neshchadim, A. A. Simonov","doi":"10.1134/S1990478923040129","DOIUrl":null,"url":null,"abstract":"<p> We study the system of equations obtained on the basis of the relativistic\nSchrödinger equation and relating the potential, amplitude, and phase functions. Using\nthe methods of the theory of consistency of systems of partial differential equations, we obtain\ncompletely integrable systems that relate only two functions of the above three. The systems\nfound are related by Bäcklund transformations.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"828 - 841"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040129","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We study the system of equations obtained on the basis of the relativistic
Schrödinger equation and relating the potential, amplitude, and phase functions. Using
the methods of the theory of consistency of systems of partial differential equations, we obtain
completely integrable systems that relate only two functions of the above three. The systems
found are related by Bäcklund transformations.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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