Among the most interesting results in classical and quantum field theory concern special nondissipative solutions of nonlinear wave equations, lumped colloquially together under the name “solitons”. Such solutions have found exciting and diverse application in physics, mathematics, and engineering related to nonlinear wave phenomena, from the very rich geometric description of their moduli spaces, to the forefront of high-bandwidth digital communications.
The topic of wave propagation on noncommutative spaces turns out to be unexpectedly relevant [1]. Among the more exciting results [2] reported in the physics literature (and studied extensively since) were those which asserted the existence of soliton solutions of nonlinear perturbations of the scalar wave equation on quantized spacetimes, a situation which does not occur for non-quantized spacetimes above dimension 1 + 1.
Practical applications of solitons in engineering signal processing exist already [3] and more are anticipated.
– Yon Visell - 04 Aug 2003
[1] J. Bertrand, P. Bertrand, Symbolic Calculus on the Time-Frequency Half-Plane, J. Math. Phys 39, No. 8 (1988). D. Gabor, Theory of Communication. J. Inst. Electr. Eng. 93 (1946) 429-457.
[2] R. Gopakumar, S. Minwalla, and A. Strominger, Noncommutative Solitons, J. High Energy Phys. 05 (2000) 20. hep-th/0003160. R. J. Szabo, Quantum Field Theory on Noncommutative Spaces, Phys Rep (To Appear). hep-th/0109162.
[3] A. C. Singer, A. V. Oppenheim, Circuit Implementations of Soliton Systems, Int J Bifurcations and Chaos 9 (4), 1999. A. C. Singer, A. V. Oppenheim, G. W. Wornell, Detection and Estimation of Multiplexed Soliton Signals, IEEE Trans Signal Proc Vol. 47 (10) 1999.