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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\phi _0(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is obtained. Further, we prove the instability of solutions around <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\phi _0(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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

  • 期刊论文

  • 发表日期：

    2025年12月13日

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  • Lijia Han,
  • Yue Qiu,
  • Xiaohong Wang

摘要

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 \(\phi _0(x)\) ϕ 0 ( x ) is obtained. Further, we prove the instability of solutions around \(\phi _0(x)\) ϕ 0 ( x ) .