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

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dc.contributor.authorCamassa, R.
dc.contributor.authorFalqui, G.
dc.contributor.authorOrtenzi, G.
dc.contributor.authorPedroni, M.
dc.date.accessioned2025-12-05T09:27:05Z
dc.date.issued2019
dc.description.abstractSelf-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 for to construction of explicit solutions by quadratures and provide the bi-Hamiltonian formulation for the reduced ODEs.
dc.description.sponsorshipRC and MP thank the Dipartimento di Matematica e Applicazioni of Universitá Milano-Bicocca for its hospitality. GF, GO, and MP thank the Carolina Center for Interdisciplinary Applied Mathematics at the University of North Carolina for hosting their visits in 2018. This work was supported by the National Science Foundation under grants RTG DMS-0943851, CMG ARC-1025523, DMS-1009750, DMS-1517879, the Office of Naval Research under grants N00014-18-1-2490 and DURIP N00014-12-1-0749. This project has also received funding under grant H2020-MSCA-RISE-2017 Project No. 778010 IPaDEGAN. All authors gratefully acknowledge the auspices of the GNFM Section of INdAM under which part of this work was carried out. Finally, thanks are also due to the anonymous referees for useful comments and suggestions for further references (e.g., [7, 31, 34]). Their work improved the final form of the present paper.
dc.identifier.citationOn 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.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2019.087
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 37K05; 37J15; 76M55
dc.identifier.otherarXiv: 1907.10920
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210301
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleOn the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations
dc.typeArticle

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