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Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a…
In the present work, we consider the existence and spectral stability of standing wave solutions to a model for light propagation in a twisted multi-core fiber with no gain or loss of energy. Numerical parameter continuation experiments…
We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schr\"odinger type is coupled to an equation of Korteweg-de Vries type. Such systems model…
We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial…
In this paper, we consider the nonlinear fractional Schr\"odinger equations with Hartree type nonlinearity. We obtain the existence of standing waves by studying the related constrained minimization problems by applying the…
We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…
Theoretical comment for the registration of longitudinal electric waves in interacting laser beams is given. Recent information on longitudinal electric and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures is…
We introduce a new notion of linear stability for standing waves of the nonlinear Schr\"odinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate…
In this brief communication, we present an exact analytic nonlinear dispersion relation (NLDR) for the dust acoustic waves using the Korteweg-de Vries (KdV) model. The NLDR agrees with the spectrum of spatio-temporal evolution obtained from…
A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…
The single-wave model equations are transformed to an exact hydrodynamic closure by using a class of solutions to the Vlasov equation corresponding to the waterbag model. The warm fluid dynamic equations are then manipulated by means of the…
Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of the structure. Can nonlinear waves help us to control the…
In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schr\"odinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained…
The linear response of an isolated, homogeneous granular fluid to small spatial perturbations is studied by methods of non-equilibrium statistical mechanics. The long wavelength linear hydrodynamic equations are obtained, with formally…
The profile of a nonlinear stationary thermomagnetic wave in the resistive state of superconductors is studied at different transport currents. It is proved that the thermomagnetic wave has an oscillating profile at relatively high values…
A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato's variable norm technique and the Fixed-Point…
This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier-Stokes equations in the half line. This is one of the series of papers by the authors on the stability of nonlinear waves…
The propagation of a wave-packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schr\"odinger equation (Gross-Pitaevskii equation). This problem is directly connected to…