2023/01/18 by Charlier, Christophe, Lenells, Jonatan
#35G20 #35Q15 #37K15 #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2301.07620
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.