Singularity formation for a nonlinear variational sine-Gordon equation in a multidimensional space

Fengmei Qin; Kyungwoo Song; Qin Wang

doi:10.4134/BKMS.b220859

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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

Singularity formation for a nonlinear variational sine-Gordon equation in a multidimensional space

Fengmei Qin, Kyungwoo Song, Qin Wang

Yunnan University; Kyung Hee University; Yunnan University

Abstract

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Abstract

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).