We review the work on exploding dissipative solitons in one and two spatial dimensions.
Features covered include: the transition from modulated to exploding dissipative solitons …

We show the existence of periodic exploding dissipative solitons. These nonchaotic
explosions appear when higher-order nonlinear and dispersive effects are added to the …

When chromatic dispersion operates together with two-dimensional diffraction, the
degenerate optical parametric oscillator exhibits three-dimensional (3D) localized structures …

We investigate a two-dimensional extended system showing chaotic and localized
structures. We demonstrate the robust and stable existence of two types of exploding …

We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a “simple”
and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in …

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 …

We study the influence of an analog of self–steepening (SST), which is a term breaking the
T→− T symmetry, on explosive localized solutions for the cubic–quintic complex Ginzburg …

Solitons, which describe the propagation of concentrated beams of light through nonlinear
media, can exhibit a variety of behaviors as a result of the intrinsic dissipation, diffraction …

We study numerically the formation of localized superlattices in spatially distributed systems.
We predict that in wide regions of the parameter space, stable localized, either bright or …

We show that for a large range of approach velocities and over a large interval of stabilizing
cubic cross-coupling between counterpropagating waves, a collision of stationary pulses …