Related papers: Two-component breather solution of the nonlinear w…
We consider a damped, parametrically driven discrete nonlinear Klein-Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces…
We further generalize the generalized short pulse equation studied recently in [Commun. Nonlinear Sci. Numer. Simulat. 39 (2016) 21-28; arXiv:1510.08822], and find in this way two new integrable nonlinear wave equations which are…
We present new solutions to the nonautonomous nonlinear Schroedinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical…
We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the…
Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy…
Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The frequency of perturbation varies slowly and passes through a resonance. The resonance generates a solitary packets of waves. Full…
The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We consider the dynamics of weakly nonlinear wave packets, and…
Specific solutions of the nonlinear Schr\"odinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the…
Evolution of the nonequilibrium inhomogeneities and topological defects is studied in terms of complex kink solutions of the sine-Gordon equation. The weakly damped oscillation of the sine-Gordon kink, named as the kink quasimode, is…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…
The solution of the wave equation in the envelope approximation with temporal corrections for a laser pulse propagating in a medium where the Kerr effect, field ionization, and associated absorption take place, is obtained through a…
In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schr\"odinger equation with several higher-order nonlinear effects representing…
The existence and properties of envelope solitary waves on a periodic, traveling wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed point computational…
Nonlinear electrodynamics model in hypercomplex form is considered. Its linearization around a solution is obtained. The appropriate problem for linear waves around static dyon solution (SDS) of Born-Infeld electrodynamics is investigated.…
We study a variable-coefficient nonlinear Schr\"odinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multi-peak…
We consider the interactions of traveling localized wave solutions with a vertex in a star graph domain that describes multiple Josephson junctions with a common/branch point (i.e., tricrystal junctions). The system is modeled by the…
Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the…
We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link…
We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on…