A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit ultra-hyperbolic selfdual vacuum spaces admiting only one Killing vector which is not selfdual, we also give the corresponding explicit Einstein–Weyl structures.

Decays of η and η ′ within a chiral unitary approach Various decays of η and η ′ are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving sand p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Sa...

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac’s equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body. PA...

Using the Nikiforov-Uvarov method, an application of the relativistic Duffin-Kemmer-Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived the first-order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using of the Nikiforov-Uvarov method that can be written ...

In this paper, we introduce a new set of vector fields for the relativistic transport equation, which is applicable general Vlasov-wave type coupled systems. By combining strength Klainerman field method and Fourier method, prove global regularity scattering 3D massive Vlasov–Nordström system small initial data without any compact support assumption, widely used in literature study Vlasov equat...

The hadronic decays η, η ′ → 3π and η ′ → ηππ are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving sand p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good overall ...

We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell’s equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Loren...

The SDiff(2) Toda equation appears in several fields of physics. Its algebra of symmetries is the area-preserving diffeomorphisms of a 2-surface, isomorphic to the algebra of Poisson brackets generated by Hamiltonian vector fields in 2 variables. These facts have allowed various researchers to create “zero-curvature representations” and even to create a formal presentation of a general solution...