Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SINGULARITY FORMATION FOR A NONLINEAR VARIATIONAL SINE-GORDON EQUATION IN A MULTIDIMENSIONAL SPACE

  • Fengmei Qin (Department of Mathematics Yunnan University) ;
  • Kyungwoo Song (Department of Mathematics College of Science Kyung Hee University) ;
  • Qin Wang (Department of Mathematics Yunnan University)
  • Received : 2022.12.17
  • Accepted : 2023.03.21
  • Published : 2023.11.30
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Abstract

We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

Keywords

Acknowledgement

The research of Qin Wang is supported by National Natural Science Foundation of China (12261100, 11761077) and NSF of Yunnan province (2019FY003007); the research of Kyungwoo Song is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1F1A1057766).

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