Related papers: Integrability meets the charged relativistic parti…
It is shown that the use of extended sets of irreducible representations of the Lorentz group opens new possibilities for the theory of relativistic wave equations from the point of view of the space-time description of both the internal…
Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particlar space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
We discuss spherically symmetric solutions for point-like sources in Lorentz-breaking massive gravity theories. This analysis is valid for St\"uckelberg's effective field theory formulation, for Lorentz Breaking Massive Bigravity and…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…
Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field…
The outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and nonsingular. For the derivative Schrodinger…
We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…
A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
We consider a problem of electron motion in different media and magnetic field. It is shown that in case of nonmoving medium and constant homogenious magnetic field the electron energies are quantized. We also discuss the general problem of…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
We study a family of equations defined on the space of tensor densities of weight $\lambda$ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the…
This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…
Particles are injected to a large planar rectangle through the boundary. Assuming that the particles move independently from one another and the boundary is also absorbing, we identify a set of abstract conditions which imply the local…
Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum…