Bright and dark soliton solutions for variable-coefficient diffusion-reaction and modified Korteweg-de Vries equations

Bekir A., Aksoy E., Guner O.

PHYSICA SCRIPTA, vol.85, no.3, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.1088/0031-8949/85/03/035009
  • Journal Name: PHYSICA SCRIPTA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Eskisehir Osmangazi University Affiliated: Yes


In this paper, by using a solitary wave ansatz in the form of sech(p) and tanh(p) functions, we obtain the exact bright and dark soliton solutions for the considered model, respectively. The topological (dark) and non-topological (bright) soliton solutions to the variable-coefficient diffusion-reaction equation and the variable-coefficient modified Korteweg-de Vries equation with power law nonlinearity are obtained by using the solitary wave ansatz method. The parametric conditions for the formation of soliton pulses are determined. Note that it is always useful and desirable to construct exact analytical solutions, especially soliton-type envelope ones, for understanding most nonlinear physical phenomena.