Standing wave solutions and instability for the Logarithmic Klein-Gordon equation
In this paper, we study the standing wave solutions of Klein--Gordon equation with logarithmic nonlinearity. The existence of the standing wave solution related to the ground state $\phi_0(x)$ is obtained. Further, we prove the instability of solutions around $\phi_0(x)$.
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| Sprache: | eng |
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| Zusammenfassung: | In this paper, we study the standing wave solutions of Klein--Gordon equation
with logarithmic nonlinearity.
The existence of the standing wave solution related to the ground state
$\phi_0(x)$ is obtained. Further, we prove the instability of solutions around
$\phi_0(x)$. |
|---|---|
| DOI: | 10.48550/arxiv.2402.11546 |