Stability theory for solitary-wave solutions of scalar field equations (Q798532)
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scientific article; zbMATH DE number 3869863
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability theory for solitary-wave solutions of scalar field equations |
scientific article; zbMATH DE number 3869863 |
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Stability theory for solitary-wave solutions of scalar field equations (English)
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1982
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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.
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stability
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travelling-wave
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solitary-wave
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classical scalar field equations
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instability
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fixed points
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