Large‐time asymptotics to the focusing nonlocal modified Kortweg‐de Vries equation with step‐like boundary conditions

نویسندگان

چکیده

We investigate the large-time asymptotics of solution for Cauchy problem nonlocal focusing modified Kortweg-de Vries (MKdV) equation with step-like initial data, i.e., $u_0(x)\rightarrow 0$ as $x\rightarrow-\infty$, A$ $x\rightarrow+\infty$,where $A$ is an arbitrary positive real number. firstly develop direct scattering theory to establish basic Riemann-Hilbert (RH) associated data. Thanks symmetries $x\rightarrow-x$, $t\rightarrow-t$ MKdV equation, we $t\rightarrow-\infty$ and $t\rightarrow+\infty$ respectively. Our main technique use steepest descent analysis deform original matrix-valued RH corresponded regular problem, which could be explicitly solved. Finally obtain different asymptotic behaviors in space-time sectors $\mathcal{R}_{I}$, $\mathcal{R}_{II}$, $\mathcal{R}_{III}$ $\mathcal{R}_{IV}$ on whole $(x,t)$-plane.

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ژورنال

عنوان ژورنال: Studies in Applied Mathematics

سال: 2023

ISSN: ['0022-2526', '1467-9590']

DOI: https://doi.org/10.1111/sapm.12568