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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• ISSN: 1815-0659
• Main Authors: Camassa, R., Falqui, G., Ortenzi, G., Pedroni, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210301
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations / R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 35 назв. — англ.

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...