Related papers: New Relativistic Wave Equations for Two-Particle S…
In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the…
Starting from first principles and general assumptions based on the energy-momentum relation of the Special Theory of Relativity we present a novel wave equation for ultrarelativistic matter. This wave equation arises when particles satisfy…
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…
Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…
This paper presents a new approach for the computation of eigenvalues of the generalized spheroidal wave equations. The novelty of the present method is in the use of the analytical derivatives of the eigenvalues to minimize losses in…
The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the $4\times 4$ matrix wave function in terms of one of the $2\times 2$ components, to a single equation of the…
In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit…
In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The…
We consider (2+1) and (1+1) dimensional long-wave short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lam\'e polynomials of order one and two. The periodic…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.
We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body…
Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schroedinder…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
A stationary wave pattern occurring in a flow of a two-component Bose-Einstein condensate past an obstacle is studied. We consider the general case of unequal velocities of two superfluid components. The Landau criterium applied to the…
A study of binary systems composed of two point particles with different masses in the linear regime of the characteristic formulation of general relativity in a Minkowski background is provided. The present paper generalizes a previous…
We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb…