Premium
Linear Stability of Solitary Waves for the One‐Dimensional Benney–Luke and Klein–Gordon Equations
Author(s) -
Stanislavova Milena
Publication year - 2015
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12062
Subject(s) - stability (learning theory) , linear stability , mathematical analysis , physics , klein–gordon equation , wave equation , classical mechanics , mathematics , traveling wave , mathematical physics , instability , mechanics , nonlinear system , quantum mechanics , machine learning , computer science
The linear stability of the solitary waves for the one‐dimensional Benney–Luke equation in the case of strong surface tension is investigated rigorously and the critical wave speeds are computed explicitly. For the Klein–Gordon equation, the stability of the traveling standing waves is considered and the exact ranges of the wave speeds and the frequencies needed for stability are derived. This is achieved via the abstract stability criteria recently developed by Stanislavova and Stefanov.