Related papers: Calculating adiabatic evolution of the perturbed D…
We develop the theory of transformation of intensive initial nonlinear wave pulses to trains of solitons emerging at asymptotically large time of evolution. Our approach is based on the theory of dispersive shock waves in which the number…
The letter introduces an extended (3+1)-dimensional [(3+1)D] nonlocal cubic complex Ginzburg-Landau equation describing the dynamics of dissipative light bullets in optical fiber amplifiers under the interplay between dopants and a…
This investigation is devoted to the effects of nonadiabatic resonant dynamic tides generated in a uniformly rotating stellar component of a close binary. The companion is considered to move in a fixed Keplerian orbit, and the effects of…
The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our…
A novel third order nonlinear evolution equation governing the dynamics of high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The linear dispersion…
Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…
The Darboux transformation (DT) formulae for the derivative nonlinear Schr\"{o}dinger (DNLS) equation are expressed in concise forms, from which the multi-solitons, n-periodic solutions, higher-order hybrid-pattern solitons and some mixed…
We consider the dynamics and stability of bright soliton stripes in the two-dimensional nonlinear Schr\"odinger equation with hyperbolic dispersion, under the action of transverse perturbations. We start by discussing a recently proposed…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
We investigate soliton generation dynamics with the influence of thermal effects. Either soliton annihilation or survival can occur in different trials with the same tuning method, and a spontaneous route to soliton formation is observed.
We review some recent results concerning Gibbs measures for nonlinear Schroedinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the…
We study here the nonlinear Schrodinger Equation (NLS) as the first term in a sequence of approximations for an electromagnetic (EM) wave propagating according to the nonlinear Maxwell equations (NLM). The dielectric medium is assumed to be…
Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr\"odinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape…
The small-$x_B$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles.…
We review the recent developments of the use of the homotopy method for solving the non-linear evolution equation for the diffractive production in deep inelastic scattering. We introduce part of the non-linear corrections in the linear…
We consider the impact of anisotropic nonlocality on the arrest of the collapse and stabilization of dipole-mode (DM) solitons in two-dimensional (2D) models of optical media with the diffusive nonlinearity. The nonlocal nonlinearity is…
When we calculate gravitational waveforms from extreme-mass-ratio inspirals (EMRIs) by metric perturbation, it is a common strategy to use the adiabatic approximation. Under that approximation, we first calculate the linear metric…
We compute the rapidity distribution of the virtual photon produced in the Drell-Yan process through next-to-next-to-leading order in perturbative QCD. We introduce a powerful new method for calculating differential distributions in hard…
We show that the number of solitons produced from an arbitrary initial pulse of the simple wave type can be calculated analytically if its evolution is governed by a generalized nonlinear Schr\"{o}dinger equation provided this number is…
The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are…