Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

Abstract

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are symmetric and antisymmetric solitons of "broad" and "narrow" types, composite states, built as combinations of broad and narrow beams with identical or opposite signs ("unipolar" and "bipolar" states, respectively), and "single-sided" broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via eigenvalues of small perturbations, and is verified in direct simulations. Three species -narrow symmetric, broad antisymmetric, and unipolar composite states -are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak inter-channel coupling.

Conditions and Stability Analysis for Saddle-Node Bifurcations of Solitary Waves in Generalized Nonlinear Schrödinger Equations

“…Recalling that u 0 ðxÞ and wðxÞ are both real as well, we see that these perturbation-series solutions (16) give two real-valued (legitimate) solitary waves when l [ l 0 , but these solitary waves do not exist when l\l 0 . On the other hand, if hu 0 ; wi and hG 2 ; w 3 i have the opposite sign, b is purely imaginary.…”

Dynamical behavior and exact solution in invariant manifold for a septic derivative nonlinear Schrödinger equation

“…where Θ(ξ ) is given by (37), and 4 . Equations (33) and (36) give rise to the profiles of solitary waves shown in Fig.…”

“…Derivative nonlinear Schrödinger equations constitute a class of models which describe the evolution in physical media that has been drawn considerable attention both in a theoretical context and in many applied disciplines, notably in hydrodynamics, nonlinear optics and the study of Bose-Einstein condensates [1][2][3][4].…”

“…Moreover, nonlinear Schrödinger (NLS) equations incorporating cubic and quintic order nonlinearity are of fundamental interest in the physics of nonlinear optics [4,5]. It is natural to consider models in nonlinear dynamics combining these two features, and indeed such systems likewise have physical applications [6][7][8].…”

Symmetry breaking and manipulation of nonlinear optical modes in an asymmetric double-channel waveguide

“…It is shown that the coupler can support the symmetry-preserving solutions which have the linear counterparts and the symmetry-breaking solutions without any linear counterparts [34][35][36], in which the spontaneous symmetry-breaking has been experimentally demonstrated in optically induced lattices with a local double-well potential [34].…”