Abstract. We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.

Key words: Solitons Monopoles and Instantons; Non-Commutative Geometry

E-print number: hep-th/0408190
Cited: by
Refers: to

Received 3 September 2004, accepted for publication 21 October 2004
Published 16 November 2004