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On the Small-Amplitude Long Waves in Linear Shear Flows and the Camassa–Holm Equation

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Abstract

We compare two linearizations used in the study of small-amplitude long waves on a constant vorticity flow. For the propagation of such waves, we derive, by a variational approach in the Lagrangian formalism, the nonlinear Camassa–Holm equation.

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Authors and Affiliations

  1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit No. 6, P.O. Box 1-764, 014700, Bucharest, Romania

    Delia Ionescu-Kruse

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  1. Delia Ionescu-Kruse
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Correspondence to Delia Ionescu-Kruse.

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Communicated by A. Constantin

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Ionescu-Kruse, D. On the Small-Amplitude Long Waves in Linear Shear Flows and the Camassa–Holm Equation. J. Math. Fluid Mech. 16, 365–374 (2014). https://doi.org/10.1007/s00021-013-0156-z

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