Exact solutions of the multidimensional derivative nonlinear Schrodinger equation for many-body systems of criticality

The authors investigate the problem of strongly interacting many-body systems near criticality as recently described in terms of nonlinear dynamics by Dixon and Tuszynski (1989). They show that in the first order of approximation, the equation of motion for the order parameter can be mapped on the derivative nonlinear Schrodinger equation and thus can be solved exactly. They solve the equations both in the absence and presence of current densities.

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