Related papers: Einstein-Infeld-Hoffman method and soliton dynamic…
We consider the nonlinear Schr\"{o}dinger equation with a point-like source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, for the given value of the potential strength and the…
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
We study stationary axially symmetric solutions of the Einstein vacuum field equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. We…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a…
We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution.…
We consider the mean-field vortex solutions and their stability within a two-component Bose Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
In this paper we study dynamics of solitons in the generalized nonlinear Schr\"odinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are…
We study the dynamics of fundamental and vortex solitons in the framework of the nonlinear Schr\"{o}dinger equation with the spatial dimension $D\geqslant 2$ with a multiplicative random term depending on the time and space coordinates. To…
With a special Lorentz-M{\o}ller-Nelson (LMN) transformation found transformation of velocity from the laboratory system S to an accelerated, rotating frame of reference s. The physical sense of parameter entering into the LMN special…
Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable…
We construct an approximate solution of field equations in the Abelian Higgs model which describes motion of a curved vortex. The solution is found to the first order in the inverse mass of the Higgs field with the help of the…
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field…