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Painlevé analysis for a new integrable equation combining the modified Calogero–Bogoyavlenskii–Schiff (MCBS) equation with its negative-order form

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Abstract

A new integrable equation is constructed by combining the recursion operator of the modified Calogero–Bogoyavlenskii–Schiff equation and its inverse recursion operator. The Painlevé is performed to demonstrate the complete integrability of the newly developed equation. Multiple-soliton solutions are depicted as manifestation of the integrability. We further show that this equation enjoys a variety of soliton solutions that include kinks, peakon, cuspon.

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Acknowledgements

The author sincerely and genuinely thanks Professor Willy Hereman for useful discussions and for using the MACYSMA package to test the Painlev’e property.

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  1. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

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  1. Abdul-Majid Wazwaz
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Correspondence to Abdul-Majid Wazwaz.

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Wazwaz, AM. Painlevé analysis for a new integrable equation combining the modified Calogero–Bogoyavlenskii–Schiff (MCBS) equation with its negative-order form. Nonlinear Dyn 91, 877–883 (2018). https://doi.org/10.1007/s11071-017-3916-0

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  • DOI: https://doi.org/10.1007/s11071-017-3916-0

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