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A Lax Representation of the Charney–Obukhov Equation for the Ocean

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Abstract

We find a Lax representation of the 4D Charney–Obukhov equation for the ocean in the \(\beta\)-plane approximation. We prove that a parameter involved in the Lax representation is non-removable. Then we derive a special Bäcklund transformation for the equation under the study.

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ACKNOWLEDGMENTS

I am very grateful to I.S. Krasil’shchik for important discussions. Computations were supported by the Jets software [23].

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, 117997, Moscow, Russia

    O. I. Morozov

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  1. O. I. Morozov
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Correspondence to O. I. Morozov.

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(Submitted by I. S. Krasil’shchik)

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Morozov, O.I. A Lax Representation of the Charney–Obukhov Equation for the Ocean. Lobachevskii J Math 44, 3973–3975 (2023). https://doi.org/10.1134/S199508022309024X

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  • DOI: https://doi.org/10.1134/S199508022309024X

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