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Inferring nonlinear parabolic field equations from modulus data

Rotha P. Yu·David M. Paganin·Michael J. Morgan
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Abstract

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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Rotha P. Yu, David M. Paganin, Michael J. Morgan. 2004-11-26. Inferring nonlinear parabolic field equations from modulus data. https://doi.org/10.1016/j.physleta.2005.04.065

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