Nonlinear-Diffusion (Burgers) and Quasioptics Equations. Projective and Lens Transformations

IF 0.8 4区地球科学 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC

Radiophysics and Quantum Electronics Pub Date : 2024-03-27 DOI:10.1007/s11141-024-10299-7

S. N. Gurbatov

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.

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非线性扩散（布尔格斯）和准光学方程。投影和透镜变换

我们讨论了布尔格斯方程的精确解（科尔-霍普夫解）与准光学抛物线方程的渐近解（几何光学近似）之间的共同属性和差异。这说明了如何应用修正透镜变换（塔拉诺夫变换）来考虑具有本质上不同时间尺度的强声波非线性相互作用的几个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Radiophysics and Quantum Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED

CiteScore

1.10

自引率

12.50%

发文量

审稿时长

6-12 weeks

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.