We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of...

In this paper the interaction of attosecond laser pulses with matter is investigated. The scattering and potential motion of heat carriers as well as the external force are considered. Depending on the ratio of the scatterings and potential motion the heat transport is described by the thermal forced Klein-Gordon or thermal modified telegraph equation. For thermal Heisenberg type relation V τ ∼...

This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange variational technique in the Riesz derivative sense and derives an approximate solitary wave solution. Our results witness that He’s variational iteration method was very efficient and powerful technique in finding the solution of the proposed equation. The basic idea described in this paper is...

We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a timedependent inner product. We apply our general results t...

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic mechanical differential equation the presence of Dunkl operator-based deformation and investigate solutions for two important problems three-dimensional spatial space. To end, after introducing mechanics, examine Dunkl–Klein–Gordon oscillator with Cartesian spherical coord...

We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positivefrequency solutions. Our method has a much wider domain of application and may be used to obtain the most general invariant inner-product on th...

In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a onedimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on so...

The properties of the deformed bosonic oscillator, and the quantum groups Uq(SL(2)) and GLq(2) in the limit as their deformation parameter q goes to a root of unity are investigated and interpreted physically. These properties are seen to be related to fractional supersymmetry and intrinsic anyonic spin. A simple deformation of the Klein-Gordon equation is introduced, based on GLq(2). When q is...

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein–Gordon equation can be used as numerical algorit...

The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that, in an appropriate probability space, the difference between the average of all solutions that satisfy certain constraints at time t = 0 and the average computed by an approximate method is small with high probability.