Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I. The Cauchy problem

被引:15
作者
Dobrokhotov, S. Yu. [1 ]
Sinitsyn, S. O.
Tirozzi, B.
机构
[1] RAS, Inst Problems Mech, Moscow 117901, Russia
[2] Moscow State Inst Elect & Math, Moscow, Russia
[3] Univ Roma La Sapienza, Dept Phys, Rome, Italy
基金
俄罗斯基础研究基金会;
关键词
Mathematical Physic; Cauchy Problem; Asymptotic Expansion; Solitary Wave; Asymptotic Solution;
D O I
10.1134/S1061920807010037
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We present a systematic study of the construction of localized asymptotic solutions of the one-dimensional wave equation with variable velocity. In part I, we discuss the solution of the Cauchy problem with localized initial data and zero right-hand side in detail. Our aim is to give a description of various representations of the solution, their geometric interpretation, computer visualization, and illustration of various general approaches (such as the WKB and Whitham methods) concerning asymptotic expansions. We discuss ideas that can be used in more complicated cases (and will be considered in subsequent parts of this paper) such as inhomogeneous wave equations, the linear surge problem, the small dispersion case, etc. and can eventually be generalized to the 2-(and n-) dimensional cases.
引用
收藏
页码:28 / 56
页数:29
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