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 fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

Since the classical dynamical r-matrix [1] first appeared on the scene of integrable many body system, many dynamical r-matrices have been found in integrable models such as CalogeroMoser model [2], Sine-Gorden soliton case [3] and the general case for the Ruijsenaars systems [4]. These dynamical r-matrices do not satisfy the ordinary classical Yang-Baxter equation, so its quantization is rathe...

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...

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...

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon equation at second order in closed form in terms of gaugeinvariant perturbations of the fields in the uniform curvature gauge. We also give a simplified form of th...