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arXiv · 2301.07620

Miura transformation for the "good'' Boussinesq equation

Christophe Charlier·Jonatan Lenells
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Abstract

It is well-known that each solution of the mKdV equation gives rise, via the Miura transformation, to a solution of the KdV equation. In this work, we show that a similar Miura-type transformation exists also for the ``good'' Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann--Hilbert problems and this is in fact how we construct the new transformation.

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Christophe Charlier, Jonatan Lenells. 2023-01-18. Miura transformation for the "good'' Boussinesq equation. https://arxiv.org/abs/2301.07620

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