Inferring nonlinear parabolic field equations from modulus data

Details Inferring nonlinear parabolic field equations from modulus data Inferring nonlinear parabolic field equations from modulus data

2004-11-26

arxiv.org/abs/cond-mat/0411663v1

Physics

Condensed Matter

Other Condensed Matter

13 pages, 3 figures

Scientific paper

10.1016/j.physleta.2005.04.065

We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three closely-spaced planes. The formalism is tested by recovering nonlinear interactions and the associated equation of motion from simulated data for a range of (2+1)-dimensional nonlinear systems, including those which exhibit spontaneous symmetry breaking. The technique is of broad applicability, being able to infer a wide class of partial differential equations, which govern systems ranging from nonlinear optics to quantum fluids.

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