Related papers: Eigen Equation of the Nonlinear Spinor
This paper is a continuation of the paper by S.P.Novikov in Funct.Anal.Appl., v.24(1990), No 4, pp 196-206. String equation is by definition the equation $[L,A]=1$ for the coefficients of two linear ordinary differential operators $L$ and…
The Finslerian curvature is introduced in the three-dimensional isospin space, suggesting that the isospin-pion field transforms according to non-linear Finslerian invariance transformations. The fundamental non-linear realization is…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis…
By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the non-relativistic limit and in the thin-layer quantization formalism. We obtain a pseudo-magnetic field and an…
The exact solutions of the Dirac equation in an external non-abelian SU(N) gauge field which is in the form of a plane wave on the light cone is obtained. The whole set of the solutions for both particles and anti-particle is constructed.
We survey a new approach to the duality-invariant systems of nonlinear electrodynamics, based on introducing auxiliary bi-spinor fields. In this approach, the entire information about the given self-dual system is encoded in the U(1)…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs consisting of three bonds. It is shown that the…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…
On a pseudo-Riemannian manifold $\mathcal{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of…
A non perturbative numerical method for determining the discrete spectra is deduced from the classical analogue of the Schrodinger's equation. The energy eigenvalues coincide with the bifurcation parameters for the classical orbits.
We carry out a constructive review of non-standard solutions of relativistic wave equations. Such solutions are obtained via splitting of relativistic wave equations written in spinor form. All these solutions are also solutions of the…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
Exact solutions of Schroedinger and Pauli equations for charged particles in an external stationary electromagnetic field of an arbitrary configuration are constructed. Green functions of scalar and spinor particles are calculated in this…
In the framework of extended nonlinear Schrodinger equation (ENSE) the classification of self-similar solutions by the relation between the amplitude and phase is performed. New solutions of ENSE - ``gray soliton'' and ``gray soliton…
Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
A new method of solution of the Bethe-Salpeter equation for a pseudoscalar quark-antiquark bound state is proposed. With the help of an integral representation, the results are directly obtained in Minkowski space. Dressing of Green's…