Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

Abstract

In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enable us the possibility of controlling the scattering of solitons as well as the lifetime of bound states.

Scattering of solitons in binary Bose-Einstein condensates with spin-orbit and Rabi couplings

“…We stress that the fractal scattering of solitons of systems described by (generalized) nonlinear Schrödinger equation were also verified in Refs. [55,58,59,62].…”

“…In a more complex scenario, collisions of solitary waves can show nontrivial structures since, due to the nonintegrability of the system, the collision outcome can depend on the initial conditions, presenting in some cases a fractal pattern [53][54][55][56][57][58][59][60][61][62]. Fractal structures in collisions of solitons are also reported in systems described by other models, such as, in the φ 4 model [63,64], the sine-Gordon model [65][66][67][68][69], etc.…”

Dynamics of localized solutions in three core coupled waveguides with quasi-periodic nonlinearity

“…Also, the fractal structures in soliton collisions were analyzed in Refs. [20,26,27,[32][33][34]. The Gross-Pitaevskii equation with a repulsive delta function potential was studied in Ref.…”

Stability of ground states of nonlinear Schrodinger systems

“…Such systems (1.1) appear in the study of interactions between short and long dispersive waves (see [1,14,14]). Moreover, numerical studies describing the dynamics of gaussons collisions of (1.1) were reported in [23]. For local well-posedness in the energy space, existence and stability of standing waves for coupled nonlinear Schrödinger system with powertype nonlinearities, the reader is referred to [2,11,12,15,20,21,5,6,7,22,3,4] and references therein.…”