Painlevé analysis and pseudopotentials of the Schamel's equation
type: Item
instance of: scholarly article
title: Painlevé analysis and pseudopotentials of the Schamel's equation
zbMATH Open document ID: 0878.35096
author: Juan-Miguel Gracia
published in: Differential Equations and Dynamical Systems
publication date: 1997-12-18T00:00:00Z
review text: The authors carry out the Painlevé analysis for the Schamel equation \[ u_t+ u^{1/2} u_x+ u_{xxx} =0. \tag{1} \] The paper consists of three sections as follows: In the first section the authors show that (1) possesses the Painlevé property. In the second section they derive the Airy equation and the Harry-Dym equation by using the \(\varphi\)-equation. In the third section the authors use the method of \textit{M. C. Nucci} [J. Phys. A 21, 73-79 (1988; Zbl 0697.35134)] to derive the pseudopotentials for (1) by means of which they construct the Lax pair.
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 989585
zbMATH Keywords: Painlevé analysis
zbMATH Keywords: pseudopotentials
zbMATH Keywords: Schamel's equation
zbMATH Keywords: Airy equation
zbMATH Keywords: Harry-Dym equation
zbMATH Keywords: Lax pair
reviewed by: Emil Minchev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 989585