Standing wave solutions and instability for the Logarithmic Klein-Gordon equation. arXiv:2402.11546
Preprint, arXiv:2402.11546 [math.AP] (2024).
Summary: 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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