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On the standing wave in coupled non‐linear Klein–Gordon equations
Author(s) -
Zhang Jian
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.340
Subject(s) - standing wave , mathematics , argument (complex analysis) , klein–gordon equation , instability , wave equation , mathematical analysis , state (computer science) , nonlinear system , physics , mechanics , quantum mechanics , biochemistry , chemistry , algorithm
Abstract This paper is concerned with the standing wave in coupled non‐linear Klein–Gordon equations. By an intricate variational argument we establish the existence of standing wave with the ground state. Then we derive out the sharp criterion for blowing up and global existence by applying the potential well argument and the concavity method. We also show the instability of the standing wave. Copyright © 2003 John Wiley & Sons, Ltd.