Special two-soliton solution of the generalized Sine–Gordon equation with a variable coefficient Academic Article uri icon


  • A new special two-soliton solution to the generalized Sine-Gordon equation with a variable coefficient is constructed analytically, by using the self-similar method and Hirota bilinear method. To construct this special solution, we do not utilize the pairs of one-soliton solutions, as is customarily done when solving the Sine-Gordon equation, but introduce two auxiliary self-similar variables in Hirota's procedure. We also study features of this solution by choosing different self-similar variables. The results obtained confirm that the behavior of such Sine-Gordon solitons can be easily controlled by the selection of the self-similar variables. © 2014 Published by Elsevier Ltd.

author list (cited authors)

  • Zhong, W., & Belić, M.

citation count

  • 11

publication date

  • December 2014