Abstract.The whole spectrum of angular parameter of matrix solutions of nonlinear wave equations is defined and multi-layer nature of matrix solutions is considered. It is shown that reduction of matrix solutions leads to contracting the spaces and composing the dimensions. Matrix solutions are used as operators of rotations to show that any vector in the matrix space can be turned to the given basis vector. A spiral of evolution is easily modelled using multi-layer nature of matrix solutions. These matrices are useful also to model a collision of helical strings, for description of vortex rings and their collision, for definition of energetic levels.

Received: April 25, 2009

AMS Subject Classification: 35Q58

Key Words and Phrases: helical string, matrix solution, nonlinear wave equation, particle collision, reduction, rotation, vortex ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 2