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We investigate the spatio-temporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe-and control fields, weaker probe pulses may propagate through the medium with…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…
Properties of two pulses propagating simultaneously in different dispersion regimes, anomalous and normal, in a Kerr-type planar waveguide are studied in the framework of the nonlinear Schroedinger equation. Catastrophic self-focusing and…
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
We study scaling properties of energy spreading in disordered strongly nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled local linear or nonlinear oscillators, and demonstrate a rather slow, subdiffusive spreading…
It is demonstrated that current theoretical models utilize equations for description of laser beam propagation in nonlinear media that were deduced under the assumption of homogeneity of dielectric constant of the media and for the case of…
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic…
We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon,…
We consider the propagation of nonlinear plane waves in porous media within the framework of the Biot-Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
In this paper, we propose a new mathematical model nonlinear reaction-diffusion PDE's describing the dynamics of propagation of cancer. Here the mixed problem for the proposed PDE's is investigated and by applying obtained results…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
Electromagnetic (EM) waves/disturbances are typically the best means to understand and analyze an ionized medium like plasma. However, the propagation of electromagnetic waves with frequency lower than the plasma frequency is prohibited by…
Electromagnetic wave propagation through cold collision free plasma is studied using the nonlinear perturbation method. It is found that the equations can be reduced to the modified Kortweg-de Vries equation.
We present a theory of electron, electromagnetic, and elastic wave propagation in systems consisting of non-overlapping scatterers in a host medium. The theory provides a framework for a unified description of wave propagation in…
We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell-Bloch equations without any approximations about the strength of the input field. We study full nonlinear…
We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of non-instantaneous correlation functions at finite particle…
A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…