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- W4380558775 abstract "We consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with non-zero boundary conditions, which can be characterized using a Riemann-Hilbert (RH) problem through the inverse scattering transform. Using the $barpartial$ generalization of the Deift-Zhou nonlinear steepest descent approach, combined with the double scaling limit technique, we obtain the long-time asymptotics of the solution of the Cauchy problem in the transition region $|x/t+6|t^{2/3}< C$ with $C>0$. The asymptotics is expressed in terms of the solution of the second Painlev'{e} transcendent." @default.
- W4380558775 created "2023-06-14" @default.
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- W4380558775 date "2023-06-12" @default.
- W4380558775 modified "2023-09-27" @default.
- W4380558775 title "Painlev'e transcendents in the defocusing mKdV equation with non-zero boundary conditions" @default.
- W4380558775 doi "https://doi.org/10.48550/arxiv.2306.07073" @default.
- W4380558775 hasPublicationYear "2023" @default.
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