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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