] o c n m p [Open Communications in Nonlinear Mathematical Physics |
Maciej Błaszak - Nonhomogeneous Dispersive Water Waves and Painlevé equations
ocnmp:7602 - Open Communications in Nonlinear Mathematical Physics, July 23, 2021, Volume 1 - https://doi.org/10.46298/ocnmp.7602Nonhomogeneous Dispersive Water Waves and Painlevé equationsArticle
Authors: Maciej Błaszak 
In this letter we consider three nonhomogeneous deformations of Dispersive Water Wave (DWW) soliton equation and prove that their stationary flows are equivalent to three famous Painlevé equations, i.e. $P_{II}$, $P_{III}$ and $P_{IV},$ respectively.
Source: arXiv.org:2106.07388
Volume: Volume 1
Published on: July 23, 2021
Accepted on: July 21, 2021
Submitted on: June 18, 2021
Keywords: Nonlinear Sciences - Exactly Solvable and Integrable Systems,Mathematics - Analysis of PDEs
Classifications
Mathematics Subject Classification 20201
- 17B68 - Virasoro and related algebras
- 34M55 - Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
- 35C08 - Soliton solutions
- 35P05 - General topics in linear spectral theory for PDEs
- 35Q35 - PDEs in connection with fluid mechanics
- 37K10 - Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
- 37K15 - Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
- 76B03 - Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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