Abstract

Numerical simulations of pulse solutions of the complex cubic--quintic Ginzburg--Landau equation (CCQGLE) reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons that are not stationary in time. Rather, they are spatially confined pulse--type structures whose envelopes exhibit complicated temporal dynamics. In this talk we will explain how these dissipative solitons occur, and using numerical simulations we will analyze their spatio-temporal behavior.

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Dissipative Solitons: Concepts and Applications to the Complex--Quintic Ginzburg--Landau Equation

Numerical simulations of pulse solutions of the complex cubic--quintic Ginzburg--Landau equation (CCQGLE) reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons that are not stationary in time. Rather, they are spatially confined pulse--type structures whose envelopes exhibit complicated temporal dynamics. In this talk we will explain how these dissipative solitons occur, and using numerical simulations we will analyze their spatio-temporal behavior.