Standing wave solutions and instability for the Logarithmic Klein-Gordon equation

2024/02/18 by Han, Lijia, Qiu, Yue, Wang, Xiaohong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.11546

Abstract

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 ϕ₀(x) is obtained. Further, we prove the instability of solutions around ϕ₀(x).

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