# IJPAM: Volume 53, No. 2 (2009)

**MULTI-LAYER NATURE OF MATRIX SOLUTIONS**

OF NONLINEAR WAVE EQUATIONS

OF NONLINEAR WAVE EQUATIONS

Institute of Mathematics and Computer Science

University of Latvia

29, Rainis Boulevard, Riga, LV-1459, LATVIA

e-mail: [email protected]

**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