A kinetic interpretation of the conservation laws of a class of completely integrable nonlinear evolution equations is obtained by introducing a distribution function depending on the spectral parameter of the inverse spectral transform of the equations. The formalism so introduced leads to a possible thermodynamical description of nonlinear and dispersive phenomena and has been applied in order to investigate the properties of the Madelung fluid associated to a nonlinear Schroedinger equation.
Kinetic and Thermodynamical Interpretation of the Conservation Laws of a Nonlinear Schroedinger Equation and other Completely Integrable Equations
PASCOLINI, ALESSANDRO
1985
Abstract
A kinetic interpretation of the conservation laws of a class of completely integrable nonlinear evolution equations is obtained by introducing a distribution function depending on the spectral parameter of the inverse spectral transform of the equations. The formalism so introduced leads to a possible thermodynamical description of nonlinear and dispersive phenomena and has been applied in order to investigate the properties of the Madelung fluid associated to a nonlinear Schroedinger equation.
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