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The integrability of an extended fifth-order KdV equation with Riccati-type pseudopotential

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Abstract

The extended fifth-order KdV equation in fluids is investigated in this paper. Based on the concept of pseudopotential, a direct and unifying Riccati-type pseudopotential approach is employed to achieve Lax pair and singularity manifold equation of this equation. Moreover, this equation is classified into three categories: extended Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation, extended Lax equation and extended Kaup–Kuperschmidt (KK) equation. The corresponding singularity manifold equations and auto-Bäcklund transformations of these three equations are also obtained. Furthermore, the infinitely many conservation laws of the extended Lax equation are found using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas.

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Acknowledgements

This work is supported by the NNSF (Nos 11275072 and 11075055), RFDP (No. 20120076110024), Innovative Research Team Program of the National Natural Science Foundation of China (No. 61021004), Shanghai Leading Academic Discipline Project (No. B412), National High Technology Research and Development Program (No. 2011AA010101) and Shanghai Knowledge Service Platform for Trustworthy Internet of Things (No. ZF1213).

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, People’s Republic of China

    YUN-HU WANG & YONG CHEN

  2. College of Art and Sciences, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China

    YUN-HU WANG

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  1. YUN-HU WANG
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  2. YONG CHEN
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Correspondence to YONG CHEN.

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WANG, YH., CHEN, Y. The integrability of an extended fifth-order KdV equation with Riccati-type pseudopotential. Pramana - J Phys 81, 737–746 (2013). https://doi.org/10.1007/s12043-013-0607-3

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  • DOI: https://doi.org/10.1007/s12043-013-0607-3

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