Riemann–Hilbert problems and the mKdV equation with step initial data: short-time behavior of solutions and the nonlinear Gibbs-type phenomenon

DOI10.1088/1751-8113/45/32/325201zbMath1256.35120OpenAlexW2021913007MaRDI QIDQ2907008

Alexander A. Minakov, Vladimir P. Kotlyarov

Publication date: 5 September 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/45/32/325201

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) PDEs with low regular coefficients and/or low regular data (35R05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (5)

Gibbs Phenomenon for Dispersive PDEs on the Line ⋮ The complex MKDV equation with step-like initial data: Large time asymptotic analysis ⋮ Maxwell–Bloch equations without spectral broadening: the long-time asymptotics of an input pulse in a long two-level laser amplifier ⋮ On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data ⋮ Initial-boundary value problem for stimulated Raman scattering model: solvability of Whitham type system of equations arising in long-time asymptotic analysis

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