[2] **viXra:1610.0278 [pdf]**
*submitted on 2016-10-23 16:35:25*

**Authors:** Yigal Gurevich

**Comments:** 8 Pages.

The method of multiple scales is applied and the second order two-scale approximation is calculated for a linear dispersive wave equation with a small perturbation proportional to the amplitude cubed.

**Category:** Functions and Analysis

[1] **viXra:1610.0244 [pdf]**
*submitted on 2016-10-21 04:28:14*

**Authors:** David Eelbode, Eckhard Hitzer

**Comments:** 16 Pages. published in Advances in Applied Clifford Algebras, 26(3), pp. 953-968 (2016), Online First: 22 Oct. 2015, DOI: 10.1007/s00006-015-0600-7.

In this paper we study Clifford Fourier transforms (CFT) of multivector functions taking values in Clifford’s geometric algebra, hereby using techniques coming from Clifford analysis (the multivariate function theory for the Dirac operator). In these CFTs on multivector signals, the complex unit i∈C is replaced by a multivector square root of −1, which may be a pseudoscalar in the simplest case. For these integral transforms we derive an operator representation expressed as the Hamilton operator of a harmonic oscillator.

**Category:** Functions and Analysis