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A new classical integrable system associated with the mKdV equation

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Abstract

In this paper, a new completely integrable system related to the spectral problem −φ xx + vφ x = λφ and the constrained flows of the mKdV equations are generated. According to the viewpoint of Hamiltonian mechanics, and based on the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system and the Hamilton equations are obtained. Moreover, by means of the constrained condition between the potential function and the eigenfunction, the involutive solutions of the mKdV equations are given.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China

    Wei Liu

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  1. Wei Liu
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Correspondence to Wei Liu.

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Liu, W. A new classical integrable system associated with the mKdV equation. Eur. Phys. J. Plus 127, 5 (2012). https://doi.org/10.1140/epjp/i2012-12005-3

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  • DOI: https://doi.org/10.1140/epjp/i2012-12005-3

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