arXiv subjects

Malomed Boris

Publications and source records attributed to Malomed Boris.

3 recordsLinked to original sources

arXiv2025

Heteronuclear and Homonuclear Vector Solitons in Lasers

Vector solitons (VSs), being observed across various fields from optics to Bose-Einstein condensates, are localized structures composed of orthogonal modes bound by nonlinear couplings. Nevertheless, the influence of intermodal linear coupling on the physical properties of this bimodal structure remains to be decently revealed and harnessed. Utilizing an ultrafast fiber laser as a platform, we predict and demonstrate that the linear mode coupling (LMC) induces the deformable VS in terms of the temporal and spectral structures. Weak LMC supports heteronuclear vector solitons built of dissimilar polarization modes, i.e., a single pulse coupled to an orthogonal damped pulse chain. On the other hand, strong LMC facilitates the homonuclear VS composed of polarization modes with similar structures, in the form of soliton compounds featuring caterpillar motions. Our findings reveal new patterns of VSs and open an effective avenue for versatile ultrafast optical sources.

physics.optics↗

arXiv2017

Solitons of the coupled Schrödinger - Korteweg - de Vries system with arbitrary strengths of the nonlinearity and dispersion

New two-component soliton solutions of the coupled high-frequency (HF) - low-frequency (LF) system, based on Schrödinger - Korteweg - de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode

nlin.PS↗

arXiv2016

Coupled solitons of intense high-frequency and low-frequency waves in Zakharov-type systems

One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schrödinger equation (NLSE) for intense HF waves to the Boussinesq (Bq) or Korteweg - de Vries (KdV) equation for the LF component through quadratic terms. The systems apply, in particular, to the interaction of surface (HF) and internal (LF) waves in stratified fluids. These solutions are two-component generalizations of the single-component Bq and KdV solitons. Perturbed dynamics and stability of the solitary waves are studied in detail by means of analytical and numerical methods. Essentially, they are stable against separation of the HF and LF components if the latter one is shaped as a potential well acting on the HF field, and unstable, against splitting of the two components, with a barrier-shaped LF one. Collisions between the solitary waves are studied by means of direct simulations, demonstrating a trend to merger of in-phase solitons, and elastic interactions of out-of-phase ones.

nlin.PS↗