This article is cited in 4 papers

Mathematical physics

Investigation of stability of supersonic solitary waves in an elastic electrically conductive micropolar material

I. B. Bakholdin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047, Moscow, Russia

Abstract: Stability of solitary waves that are solutions to one of the variants of the Boussinesq equation is investigated. This equation describes elastic waves in the presence of an electromagnetic field. The Evans function method and direct numerical solution of the equation are used to identify the instability of solitary waves. The results obtained by both methods coincided. A method for identifying instability and a method for calculating an eigenfunction that grows with time by analyzing numerical solutions of a partial differential equation are developed.

Key words: Boussinesq equation, solitary wave, stability, method of Evans function, numerical methods, elasticity, electrodynamics.

UDC: 519.63

Received: 18.03.2024
Revised: 18.03.2024
Accepted: 26.07.2024

DOI: 10.31857/S0044466924110115

 English version: Computational Mathematics and Mathematical Physics, 2024, 64:11, 2672–2679

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