Symmetry Reductions for a Generalized Fifth Order KdV Equation

Abstract

In this work, Lie symmetry analysis is performed on a generalized fifth-order KdV equation. This equation describes many nonlinear problems with great physical interest in mathematical physics, nonlinear dynamics and plasma physics, among them it is a useful model for the description of wave phenomena in plasma and solid state and internal solitary waves in shallow waters. Group invariant solutions are obtained which allow us to transform the equation into ordinary differential equations. Furthermore, taking into account the conservation laws that the ordinary differential equation admits we reduce the order of the equations. Finally, we obtain some exact solutions.

Calculating Hausdorff Dimension in Higher Dimensional Spaces

“…Fractal dimension is a leading tool to explore fractal patterns on a wide range of scientific contexts (c.f., e.g., [1][2][3]). In the mathematical literature, there can be found (at least) a pair of theoretical results allowing the calculation of the box dimension of Euclidean objects in R d in terms of the box dimension of 1-dimensional Euclidean subsets.…”