Related papers: Closed-form solutions and scaling laws for Kerr fr…
We study Kerr frequency combs and dissipative Kerr solitons in silicon photonic crystal coupled-cavity waveguides (CCW) with globally optimized dispersion at telecom wavelengths. The corresponding threshold for comb generation is found to…
In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schr\"{o}dinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The…
A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…
The nonlinear, cubic Schrodinger (NLS) equation has numerous physical applications, but in general is very difficult to solve. Nonetheless, under certain circumstances parameters quantifying the width, momentum and energy of the…
In this review we try to capture some of the recent excitement induced by experimental developments, but also by a large volume of theoretical and computational studies addressing multi-component nonlinear Schrodinger models and the…
We consider the cubic-quintic nonlinear Schr\"odinger equation: \[ i\partial_t u = -\Delta u - |u|^2u + |u|^4u. \] In the first part of the paper, we analyze the one-parameter family of ground-state solitons associated to this equation with…
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…
Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
An integrable model possessing inhomogeneous ground states is proposed as an effective model of non-uniform quantum condensates such as supersolids and Fulde--Ferrell--Larkin--Ovchinnikov superfluids. The model is a higher-order analog of…
In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and capillary effects. Formal a priori estimates show that the density of solutions to these systems should disperse…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
It is shown that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. To that end, we solve analytically the Klein-Gordon wave equation for a stationary charged massive scalar field in the background…
We study the dynamics and stability of soliton optical frequency comb generation in a dissipative, coherently pumped cavity with both second and third-order nonlinearity. Cavity sweep simulations and linear stability analysis based on path…
Frequency combs have become a prominent research area in optics. Of particular interest as integrated comb technology are chip-scale sources, such as semiconductor lasers and microresonators, which consist of resonators embedding a…
The aim of this work is to theoretically investigate the possibility of Kerr frequency combs in mechanical systems. In particular, whether microelectrome-chanical devices (MEMS) can be used to generate frequency combs in a manner that is…
We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of…
In order to describe the coupling between the Kerr nonlinearity and the stimulated Brillouin scattering, Mauger et alii recently proposed a system of partial differential equations in three complex amplitudes. We perform here its analytic…
A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schr\"{o}dinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincar\'e…