Summary
This paper is devoted to the study of the asymptotic properties of solutions of the cylindrical KdV equation. At first the behaviour of an explicit, exact solution of this equation fort → 0 andt → ∞ is given; then the long-time structure of the solution of the Cauchy problem for a generic initial condition is analysed.
Riassunto
Questo articolo è dedicato allo studio delle proprietà asintotiche di soluzioni dell’equazione di KdV cilindrica. In un primo momento si mostra il comportamento di una soluzione esplicita di questa equazione pert → 0 et → ∞; si studia quindi la struttura asintotica (t → ∞) della soluzione del problema di Cauchy, per una generica condizione iniziale.
Реэюме
Эта статья посвяшена исследованию асимптотических свойств рещений цилиндрического KdV уравнения. Сначала приводится асимптотическое поведение точного рещения зтого уравнения приt→0 и приt→∞. Затем аналиэируется структура рещения при больщих временах для проблемы Кощи при обшем начальном условии.
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Santini, P.M. Asymptotic behaviour (int) of solutions of the cylindrical KdV equation. — I. Nuov Cim A 54, 241–258 (1979). https://doi.org/10.1007/BF02899790
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DOI: https://doi.org/10.1007/BF02899790