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Perturbative Painlevé Analysis

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Future Directions of Nonlinear Dynamics in Physical and Biological Systems

Part of the book series: NATO ASI Series ((NSSB,volume 312))

Abstract

We present an improved Painlevé test, which enables us to treat negative resonances. Since the method is explained in a recent paper [5] and in proceedings elsewhere, the present version is very short. We give a brief description of the method and outline three examples.

This is an outline of the lecture given by Allan Fordy and is dedicated to Alwyn Scott for his 60th birthday.

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References

  1. M.J. Ablowitz and P.A. Clarkson, “Solitons, Nonlinear Evolution Equations and Inverse Scattering”, LMS Lecture Notes 149, CUP, Cambridge, 1991.

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  5. R. Conte, A.P. Fordy and A. Pickering, A perturbative Painlevé approach to nonlinear differential equations, preprint (1992).

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  6. A.P. Fordy and A. Pickering, Analysing negative resonances in the Painlevé test, Phys. Lett. A 160, 347–354 (1991).

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  7. A. Pickering, Testing nonlinear evolution equations for complete integrability, Ph. D. Thesis, University of Leeds (1992).

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Author information

Authors and Affiliations

  1. Service de physique de l’état condensé, Centre d’études de Saclay, F-91191, Gif-sur-Yvette Cedex, France

    Robert Conte

  2. Department of Applied Mathematical Studies and Centre for Nonlinear Studies, University of Leeds, LS2 9JT, UK

    Allan Fordy & Andrew Pickering

Authors
  1. Robert Conte
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  2. Allan Fordy
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  3. Andrew Pickering
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Editor information

Editors and Affiliations

  1. The Technical University of Denmark, Lyngby, Denmark

    P. L. Christiansen

  2. Heriot-Watt University, Edinburgh, UK

    J. C. Eilbeck

  3. University of Salerno, Baronissi, Italy

    R. D. Parmentier

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© 1993 Springer Science+Business Media New York

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Conte, R., Fordy, A., Pickering, A. (1993). Perturbative Painlevé Analysis. In: Christiansen, P.L., Eilbeck, J.C., Parmentier, R.D. (eds) Future Directions of Nonlinear Dynamics in Physical and Biological Systems. NATO ASI Series, vol 312. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1609-9_1

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  • DOI: https://doi.org/10.1007/978-1-4899-1609-9_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1611-2

  • Online ISBN: 978-1-4899-1609-9

  • eBook Packages: Springer Book Archive

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