Klein forms and the generalized superelliptic equation

Klein Forms and the Generalized Superelliptic Equation

If F (x, y) ∈ Z[x, y] is an irreducible binary form of degree k ≥ 3 then a theorem of Darmon and Granville implies that the generalized superelliptic equation F (x, y) = z has, given an integer l ≥ max{2, 7 − k}, at most finitely many solutions in coprime integers x, y and z. In this paper, for large classes of forms of degree k = 3, 4, 6 and 12 (including, heuristically, “most” cubic forms), w...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

The Explicit Gibbs-appell Equation and Generalized Inverse Forms

This paper develops an extended form of the Gibbs-Appell equation and shows that it is equivalent to the generalized inverse equation of motion. Both equations are shown to follow from Gauss's principle. An example to highlight the two equivalent, though different, equations of motion is provided. Conceptual differences between the equations, and differences in their practical application to ph...

A note on Klein-Gordon equation in a generalized Kaluza-Klein monopole background

We investigate solutions of the Klein-Gordon equation in a class of five dimensional geometries presenting the same symmetries and asymptotic structure as the Gross-Perry-Sorkin monopole solution. Apart from globally regular metrics, we consider also squashed Kaluza-Klein black holes backgrounds.