Amplitude modulations and resonant decay of excited oscillons.

We show that the decay of strongly excited oscillons in a single vacuum model reveals a chaotic, fractal-like pattern very much like the one found in kink-antikink collisions in the ϕ^{4} model. This structure can be attributed to the resonant energy transfer mechanism triggered by the modulations of amplitudes of constituent oscillons which form the excited oscillon. We also find evidence that such modulations arise as a motion of two quasibreathers inside the constituent oscillon.

Negative radiation pressure in Bose-Einstein condensates.

In two-component nonlinear Schrödinger equations, the force exerted by incident monochromatic plane waves on an embedded dark soliton and on dark-bright-type solitons is investigated, both perturbatively and by numerical simulations. When the incoming wave is nonvanishing only in the orthogonal component to that of the embedded dark soliton, its acceleration is in the opposite direction to that of the incoming wave. This somewhat surprising phenomenon can be attributed to the well-known negative effective mass of the dark soliton.

Semi-Bogomol'nyi-Prasad-Sommerfield sphaleron and its dynamics.

We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity.

Relativistic moduli space and critical velocity in kink collisions.

One important tool in the analysis of the collision of kinks and other topological solitons is the reduction of the original field theory to a finite-dimensional system of so-called collective coordinates. Here we study one recent proposal of a collective coordinate model (CCM), the perturbative relativistic moduli space (pRMS), where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyze the possibility to calculate within the pRMS the critical velocity, i.

Collective Coordinate Model of Kink-Antikink Collisions in ϕ^{4} Theory.

The fractal velocity pattern in symmetric kink-antikink collisions in ϕ^{4} theory is shown to emerge from a dynamical model with two effective moduli: the kink-antikink separation and the internal shape mode amplitude. The shape mode usefully approximates Lorentz contractions of the kink and antikink, and the previously problematic null vector in the shape mode amplitude at zero separation is regularized.

Kink-antikink collisions in a weakly interacting ϕ^{4} model.

Kink-antikink scattering in nonintegrable field theories like ϕ^{4} theory is still rather poorly understood beyond brute-force numerical calculations, even after several decades of investigation. Recently, however, some progress has been made based on the introduction of certain self-dual background fields in these field theories which imply both the existence of static kink-antikink solutions of the Bogomol'nyi type and the possibility of an adiabatic scattering (moduli space approximation). Here we continue and generalize these investigations by introducing a one-parameter family of models interpolating between the Bogomol'nyi-Prasad-Sommerfield (BPS) model with the self-dual background field and the original ϕ^{4} theory.

Spectral Walls in Soliton Collisions.

During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the effect can be seen as a hard wall from which the defect can bounce off.

Kink-antikink collisions in the φ⁶ model.

We study kink-antikink collisions in the one-dimensional nonintegrable scalar φ⁶ model. Although the single-kink solutions for this model do not possess an internal vibrational mode, our simulations reveal a resonant scattering structure, thereby providing a counterexample to the standard belief that the existence of such a mode is a necessary condition for multibounce resonances in general kink-antikink collisions. We investigate the two-bounce windows in detail, and present evidence that this structure is caused by the existence of bound states in the spectrum of small oscillations about a combined kink-antikink configuration.

Oscillon resonances and creation of kinks in particle collisions.

We present a numerical study of the process of production of kink-antikink pairs in the collision of particlelike states in the one-dimensional ϕ4 model. It is shown that there are 3 steps in the process: The first step is to excite the oscillon intermediate state in the particle collision, the second step is a resonance excitation of the oscillon by the incoming perturbations, and, finally, the soliton-antisoliton pair can be created from the resonantly excited oscillon. It is shown that the process depends fractally on the amplitude of the perturbations and the number of perturbations.