Exact solution to higher-order nonlinear equations through gauge transformation
type: Item
instance of: scholarly article
title: Exact solution to higher-order nonlinear equations through gauge transformation
zbMATH Open document ID: 0612.76002
DOI: 10.1016/0167-2789(87)90113-8
author: B. George
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: A highly nonlinear hydrodynamic equation proposed by \textit{R. S. Johnson} [Proc. R. Soc. Lond., Ser. A 357, 131-141 (1977; Zbl 0375.76017)] is solved exactly, by gauge transforming (GT) it to the mixed nonlinear Schrödinger equation. The GT is generalized further, to generate a hierarchy of integrable higher-order nonlinear systems including some known equations, along with their Lax pairs, infinite sets of conserved quantities and exact solutions.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 3991069
zbMATH Keywords: Stokes instability
zbMATH Keywords: highly nonlinear hydrodynamic equation
zbMATH Keywords: gauge transforming
zbMATH Keywords: mixed nonlinear Schrödinger equation
zbMATH Keywords: hierarchy of integrable higher-order nonlinear systems
zbMATH Keywords: Lax pairs
zbMATH Keywords: infinite sets of conserved quantities
zbMATH Keywords: exact solutions
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90113-8
OpenAlex ID: W2008526867
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description: scientific article; zbMATH DE number 3991069