{"title":"Nonlinear-Diffusion (Burgers) and Quasioptics Equations. Projective and Lens Transformations","authors":"S. N. Gurbatov","doi":"10.1007/s11141-024-10299-7","DOIUrl":null,"url":null,"abstract":"<p>We discuss the common properties of and the differences between the exact solution of the Burgers equation (the Cole–Hopf solution) and the asymptotic solution of the parabolic equation of quasioptics (the geometrical-optics approximation). It is shown how the application of the modified lens transformation (Talanov transformation) allows one to consider several problems of the nonlinear interaction of intense acoustic waves having essentially different time scales.</p>","PeriodicalId":748,"journal":{"name":"Radiophysics and Quantum Electronics","volume":"66 5-6","pages":"333 - 344"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Radiophysics and Quantum Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s11141-024-10299-7","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
We discuss the common properties of and the differences between the exact solution of the Burgers equation (the Cole–Hopf solution) and the asymptotic solution of the parabolic equation of quasioptics (the geometrical-optics approximation). It is shown how the application of the modified lens transformation (Talanov transformation) allows one to consider several problems of the nonlinear interaction of intense acoustic waves having essentially different time scales.
期刊介绍：
Radiophysics and Quantum Electronics contains the most recent and best Russian research on topics such as:
Radio astronomy;
Plasma astrophysics;
Ionospheric, atmospheric and oceanic physics;
Radiowave propagation;
Quantum radiophysics;
Pphysics of oscillations and waves;
Physics of plasmas;
Statistical radiophysics;
Electrodynamics;
Vacuum and plasma electronics;
Acoustics;
Solid-state electronics.
Radiophysics and Quantum Electronics is a translation of the Russian journal Izvestiya VUZ. Radiofizika, published by the Radiophysical Research Institute and N.I. Lobachevsky State University at Nizhnii Novgorod, Russia. The Russian volume-year is published in English beginning in April.
All articles are peer-reviewed.
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