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<p>The long-time asymptotics are obtained for finite energy solutions of the 1D Klein-Gordon equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group <i>U</i>(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Klein-Gordon equation.</p>

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Soliton type asymptotics for the Klein-Gordon equation coupled to nonlinear oscillator

  • 期刊论文

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  • 发表日期：

    2025年6月11日

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  • Elena Kopylova

摘要

The long-time asymptotics are obtained for finite energy solutions of the 1D Klein-Gordon equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Klein-Gordon equation.