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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2019, том 15, 087, 17 стр. (Mi sigma1523)

Эта публикация цитируется в 4 статьях

On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations

Roberto Camassaa, Gregorio Falquib, Giovanni Ortenzib, Marco Pedronic

a University of North Carolina at Chapel Hill, Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Chapel Hill, NC 27599, USA
b Dipartimento di Matematica e Applicazioni, Universitá di Milano-Bicocca, Milano, Italy
c Dipartimento di Ingegneria Gestionale, dell'Informazione e della Produzione, Universitá di Bergamo, Dalmine (BG), Italy

Аннотация: Self-similar solutions of the so called Airy equations, equivalent to the dispersionless nonlinear Schrödinger equation written in Madelung coordinates, are found and studied from the point of view of complete integrability and of their role in the recurrence relation from a bi-Hamiltonian structure for the equations. This class of solutions reduces the PDEs to a finite ODE system which admits several conserved quantities, which allow to construct explicit solutions by quadratures and provide the bi-Hamiltonian formulation for the reduced ODEs.

Ключевые слова: bi-Hamiltonian geometry, Poisson reductions, self-similar solutions, shallow water models.

MSC: 37K05; 37J15; 76M55

Поступила: 17 июля 2019 г.; в окончательном варианте 31 октября 2019 г.; опубликована 9 ноября 2019 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2019.087



Реферативные базы данных:
ArXiv: 1907.10920


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