Generation of \c{hi}2 solitons from the Airy wave through the parametric instability

Spontaneous creation of solitons in quadratic media by the downconversion, i.e., parametric instability against the generation of fundamental-frequency excitations, from the truncated Airy-wave (AW) mode in the second-harmonic component is studied. Parameter regions are identified for the generation of one, two, and three solitons, with additional small-amplitude "jets". Shares of the total power carried by individual solitons are found. Also considered are soliton patterns generated by the downconversion from a pair of AWs bending in opposite directions.Comment: 4 pages, 6 figures, Optics Letters, in pres

Spontaneous symmetry breaking in a nonlinear double-well structure

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta-functions, a fully analytical solution is obtained for symmetric, antisymmetric and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta-functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.Comment: submitted to Physical Review

Motion dynamics of two-dimensional fundamental and vortex solitons in the fractional medium with the cubic-quintic nonlinearity

We report results of systematic investigation of dynamics featured by moving two-dimensional (2D) solitons generated by the fractional nonlinear Schroedinger equation (FNLSE) with the cubic-quintic nonlinearity. The motion of solitons is a nontrivial problem, as the fractional diffraction breaks the Galilean invariance of the underlying equation. The addition of the defocusing quintic term to the focusing cubic one is necessary to stabilize the solitons against the collapse. The setting presented here can be implemented in nonlinear optical waveguides emulating the fractional diffraction. Systematic consideration identifies parameters of moving fundamental and vortex solitons (with vorticities 0 and 1 or 2, respectively) and maximum velocities up to which stable solitons persist, for characteristic values of the Levy index which determines the fractionality of the underlying model. Outcomes of collisions between 2D solitons moving in opposite directions are identified too. These are merger of the solitons, quasi-elastic or destructive collisions, and breakup of the two colliding solitons into a quartet of secondary ones.Comment: In the original submission of this preprint (a day ago), the title was accidentally replaced by a title of a different paper. Except for that, the preprint itself and all other details were correct. The paper will be published in Wave Motion (a special issue, "Modelling Nonlinear Waves: From Theory to Applications", dedicated to the memory of Noel F. Smyth