Stability theory for solitary-wave solutions of scalar field equations. (English) Zbl 0546.35062

The authors study the stability of special travelling-wave (solitary- wave) solutions of classical scalar field equations of the form (1) \(\square\phi +u'(\phi)=0\). They prove a stability result for a certain class of solutions of (1) under some assumptions on u. Furthermore they give a general instability result for fixed points of some nonlinear maps in a Banach space. Some applications of both theorems are discussed.
Reviewer: N.Jacob


35Q99 Partial differential equations of mathematical physics and other areas of application
35B35 Stability in context of PDEs
47H10 Fixed-point theorems
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