Akhmediev, N. and Ankiewicz, A. (2003) Solitons around Us: Integrable, Hamiltonian and Dissipative Systems. In: Porsezian, K. and Kurakose, V.C., Eds., Optical Solitons: Theoretical and Experimental Challenges, Springer, Heidelberg.

has been cited by the following article:

• TITLE: Spatio-Temporal Pulsating Dissipative Solitons through Collective Variable Methods

  AUTHORS: Olivier Asseu, Ambroise Diby, Pamela Yoboué, Aladji Kamagaté

  KEYWORDS: Dissipative Soliton, Pulsating Light Pulse, Spatiotemporal Pulses, Collective Variable Approach, Complex Cubic-Quintic Ginzburg-Landau Equation, Bifurcation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.6, June 13, 2016

  ABSTRACT: A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variational equations which give the evolution of the light pulses parameters as a function of the propagation distance. The collective coordinate approach is incomparably faster than the direct numerical simulation of the propagation equation. This allows us to obtain, efficiently, a global mapping of the 3D pulsating soliton. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics.