Maslov's complex germ in the Cauchy problem for a wave equation with a jumping velocity

DOI10.1134/S1061920822010010zbMath1490.35510OpenAlexW4293097182MaRDI QIDQ2120144

Anna I. Allilueva, Andrej I. Shafarevich

Publication date: 31 March 2022

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920822010010

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Asymptotic expansions of solutions to PDEs (35C20) Partial differential equations of mathematical physics and other areas of application (35Q99) Initial value problems for second-order parabolic equations (35K15) Initial value problems for second-order hyperbolic equations (35L15)

Cites Work

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• Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes
• Adiabatic perturbation of a periodic potential
• Reflection and refraction of Lagrangian manifolds corresponding to short-wave solutions of the wave equation with an abruptly varying velocity
• Short-wave asymptotic solutions of the wave equation with localized perturbations of the velocity
• Uniqueness theorems for solutions of exterior boundary-value problems and an analogue of St. Venant's principle
• Asymptotic soliton-form solutions of equations with small dispersion

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