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An extended modified KdV equation and its Painlevé integrability

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Abstract

In this work we present an extended higher-order modified KdV equation. An analysis is carried out to show that this equation admits the Painlevé property. For this new integrable model, the one-soliton, two-soliton and three-soliton solutions are derived by using the simplified Hirota’s direct method. We also demonstrate that one, two and three singular soliton solutions are possible for the defocusing form of this extended higher-order mKdV equation.

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Authors and Affiliations

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

    Abdul-Majid Wazwaz

  2. Department of Information Management, College of Management, Shanghai University, Shanghai, 200444, People’s Republic of China

    Gui-qiong Xu

Authors
  1. Abdul-Majid Wazwaz
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  2. Gui-qiong Xu
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Correspondence to Abdul-Majid Wazwaz.

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Wazwaz, AM., Xu, Gq. An extended modified KdV equation and its Painlevé integrability. Nonlinear Dyn 86, 1455–1460 (2016). https://doi.org/10.1007/s11071-016-2971-2

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  • DOI: https://doi.org/10.1007/s11071-016-2971-2

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