Transformations for the Camassa-Holm Equation, Its High-Frequency Limit and the Sinh-Gordon Equation.

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  • Dai Hui–Hui
    Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong
  • Pavlov Maxim
    Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong

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  • Transformations for the Camassa-Holm Eq

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In this article we present a new transformation between two integrable hierarchies of the Camassa-Holm equation and the Hunter-Saxton equation. For instance we present a transformation between the Harry-Dym equation and the extended Harry-Dym equation. Moreover, we describe a relationship between the Hunter-Saxton equation, which is the high-frequency limit of the Camassa-Holm equation, and the Sinh-Gordon equation by a reciprocal transformation.

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