Nonlinear Generalized Schrödinger’s Equations by Lifting Hamilton-Jacobi’s Formulation of Classical Mechanics
It is well known that, by taking a limit of Schrödinger’s equation, we may recover Hamilton-Jacobi’s equation which governs one of the possible formulations of classical mechanics. Conversely, we may start from the Hamilton-Jacobi’s equation and, by using a lifting principle, we may reach a set of nonlinear generalized Schrödinger’s equations. The classical Schrödinger’s equation then occurs as the simplest equation among the set.
1992 ◽
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pp. 829-844
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1994 ◽
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