Ring-shaped quasisoliton solutions of the circular symmetric 2D sine-Gordon equation

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Abstract
In this paper, the circular symmetric two-dimensional sine-Gordon equation omitting the origin is investigated by using the numerical integral method. There exists a ring-shaped quasisoliton solution and this ring-shaped wave firstly travels outward and then at certain positions it returns. A simple analytical treatment of return time is made and is in agreement with the numerical one. Finally, an interpretation of the return effect is also presented.