Bull. Korean Math. Soc. 2023; 60(6): 1697-1704
Online first article September 18, 2023 Printed November 30, 2023
https://doi.org/10.4134/BKMS.b220859
Copyright © The Korean Mathematical Society.
Fengmei Qin, Kyungwoo Song, Qin Wang
Yunnan University; Kyung Hee University; Yunnan University
We study a multidimensional nonlinear variational sine-Gor\-don 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: Singularity, variational wave equation, dipole chain
MSC numbers: Primary 35L05, 35L70
Supported by: 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 \linebreak 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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