Exploding dissipative solitons in reaction-diffusion systems

We show that exploding dissipative solitons can arise in a reaction-diffusion system for a range of parameters. As a function of a vorticity parameter, we observe a sequence of transitions from oscillatory localized states via meandering dissipative soli

Stochastic and Higher-Order Effects on Exploding Pulses

The influence of additive noise, multiplicative noise, and higher-order effects on exploding solitons in the framework of the prototype complex cubic-quintic Ginzburg-Landau equation is studied. Transitions from explosions to filling-in to the noisy spatially homogeneous finite amplitude solution, collapse (zero solution), and periodic exploding dissipative solitons are reported

Stochastic and Higher-Order Effects on Exploding Pulses

The influence of additive noise, multiplicative noise, and higher-order effects on exploding solitons in the framework of the prototype complex cubic-quintic Ginzburg-Landau equation is studied. Transitions from explosions to filling-in to the noisy spatially homogeneous finite amplitude solution, collapse (zero solution), and periodic exploding dissipative solitons are reported

Interaction of exploding dissipative solitons

We investigate the collisions of two counter-propagating exploding dissipative solitons (DSs). We demonstrate that six different outcomes can occur as a function of the nonlinear cross-coupling between the counter-propagating waves: complete interpenetration, one compound exploding DS as well as four types of two compound DSs that can be stationary, have one or two frequencies or are exploding. Since exploding DSs have been observed experimentally predominantly in nonlinear optics, we conjecture that our predictions for their interactions can be tested in laser systems

Localized structures in nonequilibrium systems

We study numerically a prototype equation which arises generically as an envelope equa- tion for a weakly inverted bifurcation associated to traveling waves: The complex quintic Ginzburg{Landau equation. We show six di erent stable localized structures including stationary pulses, moving pulses, stationary holes and moving holes, starting from lo- calized initial conditions with periodic and Neumann boundary conditions

On the stable hole solutions in the complex Ginzburg-Landau equation

We show numerically that the one-dimensional quintic complex Ginzburg-Landau equation admits four different types of stable hole solutions. We present a simple analytic method which permits to calculate the region of existence and approximate shape of stable hole solutions in this equation. The analytic results are in good agreement with numerical simulations