Summary
A reduction method is introduced for the nonlinear evolution equations associated with aN×N matrix spectral problem. It is shown that this technique, as applied to the 2×2 generalized Zakharov-Shabat spectral problem, yields the Burgers equation. This equation is then investigated within the spectral-transform method.
Riassunto
Si introduce un metodo di riduzione per le equazioni di evoluzione non lineari associate ad un problema spettrale matricialeN×N. Si mostra come questa tecnica di riduzione, quando applicata al problema spettrale generalizzato 2×2 di Zakharov-Shabat, produca l’equazione di Burgers. Si discute infine questa equazione nell'àmbito del metodo della transformata spettrale.
Резюме
Предлагается метод упрощения для нелинейных уравнений эволюциии, который связан с матричнойN×N спектральной проблемой. Показывается, что применение этой техники к 2×2 обобщенной спектральной проблеме Захарова-Щабата ириводит к уравнению Бургерса. Затем это уравнение исследуестя с помощью спектрального метода преобразования.
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Degasperis, A., Leon, J.J. Matrix spectral transform, reductions and the Burgers equation. Nuov Cim B 78, 129–155 (1983). https://doi.org/10.1007/BF02721092
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DOI: https://doi.org/10.1007/BF02721092