Related papers: Two-component breather solution of the nonlinear w…
A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schr\"odinger equations. The numerical approach allows high precision numerical studies of…
Nonlinear effects in pulse propagation through a medium consisting of four-level double-$\Lambda$-type systems are studied theoretically. We apply three continous-wave driving fields and a pulsed probe field such that they form a closed…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…
The interest in the Klein-Gordon equation with different potentials has increased in recent years due to its possible applications in Cosmology, Hadron Physics and High-Energy Physics. In this work we investigate the solutions of the…
We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…
We consider the high-order nonlinear Schr\"odinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational,…
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation \begin{align} \partial_t^2 U - \Delta U + m^2 U = \Gamma (x) U^3 \quad \text{on } \mathbb{R} \times \mathbb{R}^3, \end{align} which are…
Breathers are nontrivial time-periodic and spatially localized solutions of nonlinear dispersive partial differential equations (PDEs). Families of breathers have been found for certain integrable PDEs but are believed to be rare in…
We study quantum fluctuations of macroscopic parameters of an NLS breathers, i.e., the second-order soliton solution of the nonlinear Schr\"odinger equation. Uncertainty relations for the parameters are derived and compared to similar…
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…
We present some physically interesting, in general non-stationary, one-dimensional solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed recently. The solutions include a coherent state, a phase-modified…
Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The solutions are expressed in terms of Ince…
Breather solutions of the nonlinear Schr\"{o}dinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a…
We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that…
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…
We investigate generalized nonlocal coupled nonlinear Schroedinger equation containing Self-Phase Modulation, Cross-Phase Modulation and Four-Wave Mixing involving nonlocal interaction. By means of Darboux transformation, we obtained a…
We give the solution of the Whitham modulation equations for envelopes of pulses evolving according to the sine-Gordon equation. The Whitham equations are interpreted as the equations of relativistic hydrodynamics and their solving is…
We study a deterministic gas of breathers for the Focusing Nonlinear Schr\"odinger equation. The gas of breathers is obtained from a $N$-breather solution in the limit $N\to \infty$.\\ The limit is performed at the level of scattering data…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…