Intensity limits for stationary and interacting multi-soliton complexes

We obtain an accurate estimate for the peak intensities of multi-soliton complexes for a Kerr-type nonlinearity in the (1+1) - dimension problem. Using exact analytical solutions of the integrable set of nonlinear Schrodinger equations, we establish a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities. A clear geometrical interpretation of this effect is given.Comment: 3 pages, 3 figure

Interplay between Coherence and Incoherence in Multi-Soliton Complexes

We analyze photo-refractive incoherent soliton beams and their interactions in Kerr-like nonlinear media. The field in each of M incoherently interacting components is calculated using an integrable set of coupled nonlinear Schrodinger equations. In particular, we obtain a general N-soliton solution, describing propagation of multi-soliton complexes and their collisions. The analysis shows that the evolution of such higher-order soliton beams is determined by coherent and incoherent contributions from fundamental solitons. Common features and differences between these internal interactions are revealed and illustrated by numerical examples.Comment: 4 pages, 3 figures; submitted to Physical Revie

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms

We present the fifth-order equation of the nonlinear Schrodinger hierarchy. This integrable partial differential ¨ equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrodinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated ¨ flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.The authors acknowledge the support of the Australian Research Council (Discovery Project No. DP140100265). N.A. and A.A. acknowledge support from the Volkswagen Stiftung and A.C. acknowledges Endeavour Postgraduate Award support

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

We study light-beam propagation in a nonlinear coupler with an asymmetric double-channel waveguide and derive various analytical forms of optical modes. The results show that the symmetry-preserving modes in a symmetric double-channel waveguide are deformed due to the asymmetry of the two-channel waveguide, yet such a coupler supports the symmetry-breaking modes. The dispersion relations reveal that the system with self-focusing nonlinear response supports the degenerate modes, while for self-defocusingmedium the degenerate modes do not exist. Furthermore, nonlinear manipulation is investigated by launching optical modes supported in double-channel waveguide into a nonlinear uniform medium.Comment: 10 page

Multisoliton complexes in a sea of radiation modes

We derive exact analytical solutions describing multi-soliton complexes and their interactions on top of a multi-component background in media with self-focusing or self-defocusing Kerr-like nonlinearities. These results are illustrated by numerical examples which demonstrate soliton collisions and field decomposition between localized and radiation modes.Comment: 7 pages, 7 figure

Soliton X-junctions with controllable transmission

We propose new planar X-junctions and multi-port devices written by spatial solitons, which are composed of two (or more) nonlinearly coupled components in Kerr-type media. Such devices have no radiation losses at a given wavelength. We demonstrate that, for the same relative angle between the channels of the X-junctions, one can vary the transmission coefficients into the output channels by adjusting the polarizations of multi-component solitons. We determine analytically the transmission properties and suggest two types of experimental embodiments of the proposed device.Comment: 3 pages, 2 figure

Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation

Approximate analytical chirped solitary pulse (chirped dissipative soliton) solutions of the one-dimensional complex cubic-quintic nonlinear Ginzburg-Landau equation are obtained. These solutions are stable and highly-accurate under condition of domination of a normal dispersion over a spectral dissipation. The parametric space of the solitons is three-dimensional, that makes theirs to be easily traceable within a whole range of the equation parameters. Scaling properties of the chirped dissipative solitons are highly interesting for applications in the field of high-energy ultrafast laser physics.Comment: 20 pages, 12 figures, the mathematical apparatus is presented in detail in http://info.tuwien.ac.at/kalashnikov/NCGLE2.htm

Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation (MNLS) also known as the Dysthe equation. This numerical modelling allowed us to directly compare simulations with recent results of laboratory measurements in \cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.Comment: under revision in Physical Review

Solutions of the higher-order Manakov-type continuous and discrete equations

We derive exact and approximate localized solutions for the Manakov-type continuous and discrete equations. We establish the correspondence between the solutions of the coupled Ablowitz-Ladik equations and the solutions of the coupled higher-order Manakov equations.The authors acknowledge the support of the ARC (Discovery Project DP140100265). N.A. and A.A. acknowledge the support of the Volkswagen Stiftung, while A.C. is grateful for support through an Endeavour Fellowship

Stabilization of dipole solitons in nonlocal nonlinear media

We address the stabilization of dipole solitons in nonlocal nonlinear materials by two different approaches. First, we study the properties of such solitons in thermal nonlinear media, where the refractive index landscapes induced by laser beams strongly depend on the boundary conditions and on the sample geometry. We show how the sample geometry impacts the stability of higher-order solitons in thermal nonlinear media and reveal that dipole solitons can be made dynami-cally stable in rectangular geometries in contrast to their counterparts in thermal samples with square cross-section. Second, we discuss the impact of the saturation of the nonlocal nonlinear response on the properties of multipole solitons. We find that the saturable response also stabi-lizes dipole solitons even in symmetric geometries, provided that the input power exceeds a criti-cal value.Comment: 29 pages, 8 figures, to appear in Phys. Rev.