Painlevé test for long-wave, short-wave interaction equation. II
type: Item
instance of: scholarly article
title: Painlevé test for long-wave, short-wave interaction equation. II
zbMATH Open document ID: 0682.35093
DOI: 10.1007/BF00669298
author: Pranab K. Chanda
author: A. Roy Chowdhury
published in: International Journal of Theoretical Physics
publication date: 1988-01-01T00:00:00Z
review text: [For part I see J. Math. Phys. 27, 707-709 (1986; Zbl 0596.35111).] In part I it was discussed the integrability of a long-wave, short-wave interaction equation for very restricted values of the parameters in the framework of the theory laid down by \textit{J. Weiss}, \textit{M. Tabor} and \textit{G. Carnevale} [J. Math. Phys. 24, 522-526 (1983; Zbl 0514.35083)]. Here it is proceeded with the analysis in the sense of Weiss et al., considering values of parameters other than those used previously. It is observed that for the combination of parameters for which a Lax pair was obtained by the approach of \textit{A. C. Newell} [Proc. R. Soc. London, Ser. A 365, 283-311 (1979; Zbl 0403.35048)], the equations considered pass the Painlevé test for integrability in the sense of Weiss et al. Several other combinations of parameters that do not pass the test are discussed. For these cases no Lax pair was reported by Newell.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 4117094
zbMATH Keywords: Painlevé test
zbMATH Keywords: long-wave
zbMATH Keywords: short-wave interaction
zbMATH Keywords: integrability
zbMATH Keywords: Lax pair
reviewed by: Viorel Iftimie
MaRDI profile type: Publication
cites work: A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
cites work: Q3925229
cites work: Q3280274
cites work: Q4135943
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type
cites work: The general structure of integrable evolution equations
cites work: The weak-Painlevé property as a criterion for the integrability of dynamical systems
cites work: To the complete integrability of long-wave–short-wave interaction equations
cites work: Prolongation structures of nonlinear evolution equations
cites work: Integrable and solvable systems, and relations among them
cites work: The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
cites work: On classes of integrable systems and the Painlevé property
cites work: The sine-Gordon equations: Complete and partial integrability
cites work: The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
cites work: Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations
cites work: Bäcklund transformation and the Painlevé property
cites work: The Painlevé property for partial differential equations
cites work: Necessary condition for the existence of algebraic first integrals
cites work: Korteweg-de Vries equation: a completely integrable Hamiltonian system
description: scientific article; zbMATH DE number 4117094