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.

Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I. The Cauchy problem / Tirozzi, Benedetto; S., Yu Dobrokhotov; S., Sinitsin. - In: RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 1061-9208. - STAMPA. - 14:1(2007), pp. 28-56. [10.1134/s1061920807010037]

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

TIROZZI, Benedetto;
2007

Abstract

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.
2007
asymptotic expansion
01 Pubblicazione su rivista::01a Articolo in rivista
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I. The Cauchy problem / Tirozzi, Benedetto; S., Yu Dobrokhotov; S., Sinitsin. - In: RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 1061-9208. - STAMPA. - 14:1(2007), pp. 28-56. [10.1134/s1061920807010037]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/29507
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