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<p>The dispersive estimate plays a pivotal role in establishing the long-term behavior of solutions to the nonlinear equation, thereby being crucial for investigating the well-posedness of the equation. In this work we prove that the solutions to Klein-Gordon equation on 1-d lattices follow the dispersive estimate provided that potential is quasi-periodic with Diophantine frequencies and closed to positive constants.</p>

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Dispersive estimate for quasi-periodic Klein-Gordon equation on 1-d lattices

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Hongyu Cheng

摘要

The dispersive estimate plays a pivotal role in establishing the long-term behavior of solutions to the nonlinear equation, thereby being crucial for investigating the well-posedness of the equation. In this work we prove that the solutions to Klein-Gordon equation on 1-d lattices follow the dispersive estimate provided that potential is quasi-periodic with Diophantine frequencies and closed to positive constants.