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A fifth order semidiscrete mKdV equation

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Abstract

In this paper, aiming to get more insight on the relation between the higher order semidiscrete mKdV equations and higher order mKdV equations, we construct a fifth order semidiscrete mKdV equation from the three known semidiscrete mKdV fluxes. We not only give its Lax pairs, Darboux transformation, explicit solutions and infinitely many conservation laws, but also show that their continuous limits yield the corresponding results for the fifth order mKdV equation. We thus conclude that the fifth order discrete mKdV equation is extremely an useful discrete scheme for the fifth order mKdV equation.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Tong Zhou, ZuoNong Zhu & Peng He

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  1. Tong Zhou
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  2. ZuoNong Zhu
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  3. Peng He
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Correspondence to ZuoNong Zhu.

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Zhou, T., Zhu, Z. & He, P. A fifth order semidiscrete mKdV equation. Sci. China Math. 56, 123–134 (2013). https://doi.org/10.1007/s11425-012-4447-2

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  • DOI: https://doi.org/10.1007/s11425-012-4447-2

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