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Kinetic and thermodynamical interpretation of the conservation laws of a nonlinear Schrödinger equation and other completely integrable systems

Кинегииеская и термодинамическая интерпретация законов сохранения для нелинейного уравнения Шредингера и других полностью интегририруемых систем

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Il Nuovo Cimento B (1971-1996)

Summary

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 Schrödinger equation.

Riassunto

Attraverso una funzione di distribuzione dipendente dal parametro spettrale si dà una interpretazione cinetica delle leggi di conservazione di una classe di equazioni d’evoluzione non lineari, completamente integrabili. Il formalismo introdotto, che conduce naturalmente ad una descrizione termodinamica dei fenomeni dispersivi e non lineari, è stato impiegato nello studio delle proprietà del fluido di Madelung associato ad una equazione di Schrödinger non lineare.

Резюме

Предлагается кинетическая интерпретация законов сохранения для класса полностью интегрируемых нелинейных уравнений эволюции, вводя функцию распределения, зависящую от спектрального параметра обратного спектрального преобразования уравнений. Предложенный формализм приводит к возможному термодинамическому описаний нелинейных и диссипативных явлений и приименяется для исследования жидкости Маделунга, связанной с нелинейным уравнением Шредингера.

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Authors and Affiliations

  1. Dipartimento di Fisica dell'Università, Padova

    T. A. Minelli & A. Pascolini

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italia

    T. A. Minelli & A. Pascolini

Authors
  1. T. A. Minelli
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  2. A. Pascolini
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Minelli, T.A., Pascolini, A. Kinetic and thermodynamical interpretation of the conservation laws of a nonlinear Schrödinger equation and other completely integrable systems. Nuov Cim B 85, 1–16 (1985). https://doi.org/10.1007/BF02721517

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PACS. 03.40.

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