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Pole expansions of nonlinear partial differential equations

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Il Nuovo Cimento B (1971-1996)

Summary

Pole expansions of certain solutions of various nonlinear partial differential equations are investigated. The most interesting results obtain for the Korteweg-de Vries and especially for the Burgers-Hopf equations. The motion of the poles is shown to correspond formally to the motion of one-dimensional particles interacting via simple two-body potentials, such that the corresponding many-body problems are integrable.

Riassunto

Si analizzano sviluppi polari di certe soluzioni di varie equazioni differenziali parziali non lineari. I risultati più interessanti si ottengono per l’equazione di Korteweg-de Vries e specialmente per quella di Burgers-Hopf. Si mostra che il moto dei poli corrisponde formalmente al moto di particelle unidimensionali interagenti attraverso semplici potenziali a due corpi in modo che i corrispondenti problemi a molti corpi sono integrabili.

Резюме

Исследуетса разложение по полюсам мероморфных решений различных нелинейных уравнений в частных производных. Наиболее полные резулбтаты получены дла уравнеий Кортевега-де Фриза и Бюргерса-Хопфа, дла которых показано сведение задачи о движении полюсов к механическим задачам о движении частиц с потенциаламиx −2,x −4. Показано, что движение полюсов дла ряда уравнений описываетса гамильтоновыми системами с эллиптическим потенциалом взаимодействиа.

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Authors and Affiliations

  1. ul. Tarasovskaya 10a, ap. 17, 252033, Kiev-33, USSR

    D. V. Choodnovsky & G. V. Choodnovsky

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  1. D. V. Choodnovsky
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  2. G. V. Choodnovsky
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Choodnovsky, D.V., Choodnovsky, G.V. Pole expansions of nonlinear partial differential equations. Nuovo Cim B 40, 339–353 (1977). https://doi.org/10.1007/BF02728217

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  • DOI: https://doi.org/10.1007/BF02728217

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