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ANALYTICAL SOLUTIONS TO SINE-GORDON EQUATION WITH VARIABLE COEFFICIENT

We study exact soliton solutions of the Sine-Gordon (SG) equation with variable coefficient. Based on the similarity transformation and Hirota's bilinear method, we report both kink-type and anti-kink-type one-soliton and two-soliton solutions of the SG equation. In particular, we analyze the emerging soliton structures by a special selection of two self-similar variables. Our results show that the shapes of both kink-type and anti-kink-type solitons can be effectively controlled by the specific form of those two self-similar variables.