相关论文: Nonlinear Dirac Equations

We introduce non-linear Dirac operators in $\mathbb{R}^{n}$ associated to the $p$-harmonic equation and we extend to other contexts including spin manifolds and the sphere.

Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of…

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…

In this note we will present an extension of the Krein-Rutman theorem for an abstract nonlinear, compact, positively 1-homogeneous, monotone non-decreasing operators on a Banach space and apply the result to many nonlinear elliptic partial…

We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local…

We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…

The recent literature shows a renewed interest, with various independent approaches, in the classical theories for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…

We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic nonlinearity. We show that, with the nonlinearity parameters specifically tuned, a high degree of localization of both spinor components is enabled on a…

We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…

The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…

We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…

Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz…

After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented…

In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…

It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant…

Let $X$ be a noncomplete metric space satisfying the usual (local) assumptions of a doubling property and a Poincar\'e inequality. We study extensions of Newtonian Sobolev functions to the completion $\widehat{X}$ of $X$ and use them to…

Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and…

We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…