Boris Malomed | Tel Aviv University (original) (raw)
I am a chaired professor at the Dept. of Physical Electronics at the Tel Aviv University. My research interests include nonlinear optics, matter waves in BEC, solitons, nonlinear waves, and nonlinear dissipative patterns in various physical settings.
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Papers by Boris Malomed
Soliton "molecules", i.e., bound states of two or several solitons, represent a fundamental conce... more Soliton "molecules", i.e., bound states of two or several solitons, represent a fundamental concept, which manifests itself in various nonlinear systems. They are dynamically similar to chemical molecules, attracting great interest to fundamental studies and offering potential applications (such as multilevel encoding of optical data). Here, the study demonstrates a novel dichromatic soliton-molecule compounds (DSMC) built as a hybrid bound state of multiple bound soliton pulses carried by two wavelengths in a fiber laser. The DSMCs are maintained by two different binding mechanisms, viz., the self-phase modulation (SPM) interaction between temporal solitons at the same wavelength, mediated by their tails, and the cross-phase modulation (XPM) interaction between solitons at different wavelengths. They also exhibit unique temporal and spectral vibration profiles. Both static DSMCs and ones with robust internal vibrations are generated experimentally in the fiber laser, and numerically as solutions of the corresponding dissipative nonlinear model. The findings reported here expand the concept of soliton molecules and further promote their similarity to chemical molecules.
We address effects of interplay of two different fractional-diffraction terms, corresponding to d... more We address effects of interplay of two different fractional-diffraction terms, corresponding to different Lé vy indices (LIs), in the framework of nonlinear Schrödinger equation (NLSE) with cubic-quintic nonlinearity (dual-LI fractional NLSE), in one-and two-dimensional (1D and 2D) settings. The critical (in 1D) and supercritical (in 2D) wave collapses are suppressed in the presence of a defocusing quintic term, making it possible to produce stable localized modes, including fundamental and vortical ones. In 2D, families of fundamental and vortex solitons, with topological charges = 0, 1, 2, 3, are produced in a numerical form and by dint of the variational approximation (VA). In particular, the threshold power necessary for the existence of 2D fundamental solitons is predicted by the VA, being close to the numerical results. In the case of fractional-diffraction terms with unequal LIs acting in two transverse directions, anisotropic 2D fundamental and vortex solitons are constructed. Stability of the solitons is investigated for small perturbations governed by the linearized equations, and results are corroborated by direct simulations of the perturbed evolution. Those vortex solitons which are unstable are split by azimuthal perturbations into fragments, whose number is determined by the shape of the perturbation eigenmode with the largest growth rate. These results extend the concept of the 2D fractional diffraction and solitons to media with the anisotropic fractionality.
Excited states (ESs) of two-and three-dimensional (2D and 3D) solitons of the semivortex (SV) and... more Excited states (ESs) of two-and three-dimensional (2D and 3D) solitons of the semivortex (SV) and mixedmode (MM) types, supported by the interplay of the spin-orbit coupling (SOC) and local nonlinearity in binary Bose-Einstein condensates, are unstable, on the contrary to the stability of the SV and MM solitons in their fundamental states. We propose a stabilization strategy for these states in 3D, combining SOC and long-range Rydberg-Rydberg interactions (RRI), in the presence of a spatially-periodic potential, that may include a paritytime ()-symmetric component. ESs of the SV solitons, which carry integer vorticities and + 1 in their two components, exhibit robustness up to = 4. ESs of MM solitons feature an interwoven necklace-like structure, with the components carrying opposite fractional values of the orbital angular momentum. Regions of the effective stability of the 3D solitons of the SV and MM types (both fundamental ones and ESs), are identified as functions of the imaginary component of the -symmetric potential and strengths of the SOC and RRI terms.
It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintai... more It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spinorbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a double-layer system, in which two binary condensates, stabilized by the SOC, are linearly coupled by tunneling. By means of the numerical methods, it is found that symmetric two-layer solitons undergo the spontaneous-symmetry-breaking (SSB) bifurcation of the subcritical type. The bifurcation produces families of asymmetric 2D solitons, which exist up to the value of the total norm equal to the norm of the Townes solitons, above which the collapse occurs. This situation terminates at a critical value of the inter-layer coupling, beyond which the SSB bifurcation is absent, as the collapse sets in earlier. Symmetric 2D solitons that are destabilized by the SSB demonstrate dynamical symmetry breaking, in combination with intrinsic oscillations of the solitons, or transition to the collapse, if the soliton's norm is sufficiently large. Asymmetric MMs produced by the SSB instability start spontaneous drift, in addition to the intrinsic vibrations. Consideration of moving 2D solitons is a nontrivial problem because SOC breaks the Galilean invariance. It is found that the system supports moving MMs up to a critical value of the velocity, beyond which they undergo delocalization.
Soliton "molecules", i.e., bound states of two or several solitons, represent a fundamental conce... more Soliton "molecules", i.e., bound states of two or several solitons, represent a fundamental concept, which manifests itself in various nonlinear systems. They are dynamically similar to chemical molecules, attracting great interest to fundamental studies and offering potential applications (such as multilevel encoding of optical data). Here, the study demonstrates a novel dichromatic soliton-molecule compounds (DSMC) built as a hybrid bound state of multiple bound soliton pulses carried by two wavelengths in a fiber laser. The DSMCs are maintained by two different binding mechanisms, viz., the self-phase modulation (SPM) interaction between temporal solitons at the same wavelength, mediated by their tails, and the cross-phase modulation (XPM) interaction between solitons at different wavelengths. They also exhibit unique temporal and spectral vibration profiles. Both static DSMCs and ones with robust internal vibrations are generated experimentally in the fiber laser, and numerically as solutions of the corresponding dissipative nonlinear model. The findings reported here expand the concept of soliton molecules and further promote their similarity to chemical molecules.
We address effects of interplay of two different fractional-diffraction terms, corresponding to d... more We address effects of interplay of two different fractional-diffraction terms, corresponding to different Lé vy indices (LIs), in the framework of nonlinear Schrödinger equation (NLSE) with cubic-quintic nonlinearity (dual-LI fractional NLSE), in one-and two-dimensional (1D and 2D) settings. The critical (in 1D) and supercritical (in 2D) wave collapses are suppressed in the presence of a defocusing quintic term, making it possible to produce stable localized modes, including fundamental and vortical ones. In 2D, families of fundamental and vortex solitons, with topological charges = 0, 1, 2, 3, are produced in a numerical form and by dint of the variational approximation (VA). In particular, the threshold power necessary for the existence of 2D fundamental solitons is predicted by the VA, being close to the numerical results. In the case of fractional-diffraction terms with unequal LIs acting in two transverse directions, anisotropic 2D fundamental and vortex solitons are constructed. Stability of the solitons is investigated for small perturbations governed by the linearized equations, and results are corroborated by direct simulations of the perturbed evolution. Those vortex solitons which are unstable are split by azimuthal perturbations into fragments, whose number is determined by the shape of the perturbation eigenmode with the largest growth rate. These results extend the concept of the 2D fractional diffraction and solitons to media with the anisotropic fractionality.
Excited states (ESs) of two-and three-dimensional (2D and 3D) solitons of the semivortex (SV) and... more Excited states (ESs) of two-and three-dimensional (2D and 3D) solitons of the semivortex (SV) and mixedmode (MM) types, supported by the interplay of the spin-orbit coupling (SOC) and local nonlinearity in binary Bose-Einstein condensates, are unstable, on the contrary to the stability of the SV and MM solitons in their fundamental states. We propose a stabilization strategy for these states in 3D, combining SOC and long-range Rydberg-Rydberg interactions (RRI), in the presence of a spatially-periodic potential, that may include a paritytime ()-symmetric component. ESs of the SV solitons, which carry integer vorticities and + 1 in their two components, exhibit robustness up to = 4. ESs of MM solitons feature an interwoven necklace-like structure, with the components carrying opposite fractional values of the orbital angular momentum. Regions of the effective stability of the 3D solitons of the SV and MM types (both fundamental ones and ESs), are identified as functions of the imaginary component of the -symmetric potential and strengths of the SOC and RRI terms.
It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintai... more It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spinorbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a double-layer system, in which two binary condensates, stabilized by the SOC, are linearly coupled by tunneling. By means of the numerical methods, it is found that symmetric two-layer solitons undergo the spontaneous-symmetry-breaking (SSB) bifurcation of the subcritical type. The bifurcation produces families of asymmetric 2D solitons, which exist up to the value of the total norm equal to the norm of the Townes solitons, above which the collapse occurs. This situation terminates at a critical value of the inter-layer coupling, beyond which the SSB bifurcation is absent, as the collapse sets in earlier. Symmetric 2D solitons that are destabilized by the SSB demonstrate dynamical symmetry breaking, in combination with intrinsic oscillations of the solitons, or transition to the collapse, if the soliton's norm is sufficiently large. Asymmetric MMs produced by the SSB instability start spontaneous drift, in addition to the intrinsic vibrations. Consideration of moving 2D solitons is a nontrivial problem because SOC breaks the Galilean invariance. It is found that the system supports moving MMs up to a critical value of the velocity, beyond which they undergo delocalization.