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Extension of the spectral-transform method for solving nonlinear evolution equations and related conservation laws

Обобщение метода спектральных преобразований для решения нелинейного уравнения эволюции и законы сохранения

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Il Nuovo Cimento B (1971-1996)

Summary

The spectral-transform method for solving nonlinear evolution equations is extended to certain classes of matrix equations with linearlyx-dependent coefficients and the existence of the conservation laws for the new class of nonlinear evolution equations is investigated. A remarkably explicit representation is, moreover, obtained for the conserved quantities of the «old» classes of nonlinear evolution equations (withx-independent coefficients).

Riassunto

In questo lavoro il metodo della trasformata spettrale per risolvere equazioni di evoluzione non lineari è stato esteso a certe equazioni matriciali nelle quali compare una dipendenza lineare esplicita dalla variabile spazialex; si è studiata anche l'esistenza di leggi di conservazione associate alla nuova classe di equazioni di evoluzione non lineari. Nel processo di derivazione di tali leggi, si è ottenuta una rappresentazione esplicita notevole per le quantità conservate della «vecchia» classe di equazioni di evoluzione non lineari (cioè quelle in cui non c'è la dipendenza esplicita dalla variabile spazialex).

Резюме

Метод спектральных преобразований для решения нелинейного уранвнеия эволюции обобщается на некоторые классы матричного уравнения с коэффициентами, зависящими линейно отx. Исследуется существование законов сохранения для нового класса нелинейного уравнения эволюции. Кроме того, получается явное представление для сохраняющихся величин «старых» классов нелинейного уравнения эволюции (с коэффициентами, не зависящими отx).

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  1. Istituto di Fisica dell'Università, 00185, Roma, Italy

    L. Pilloni

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Pilloni, L. Extension of the spectral-transform method for solving nonlinear evolution equations and related conservation laws. Nuov Cim B 56, 87–109 (1980). https://doi.org/10.1007/BF02738360

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