Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 122-128 |
| Number of pages | 7 |
| Journal | Applied Mathematics Letters |
| Volume | 38 |
| DOIs | |
| Publication status | Published - Dec 2014 |
| Externally published | Yes |
Keywords
- Kink and anti-kink soliton solutions
- The generalized Sine-Gordon equation with a variable coefficient
- The self-similar method