On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves
K. Andreiev, I. Egorova
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine,
47 Nauky Ave., Kharkiv, 61103, Ukraine
We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in . In the present work, we correct the formula for the second term by investigating the corresponding parametrix problem. We also study an influence of the resonance on the asymptotical behavior of the solution.
Key words and phrases:
KdV equation, rarefaction wave, parametrix problem.
PDF file (410 kB)
MSC: 37K40, 35Q53, 35Q15
K. Andreiev, I. Egorova, “On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves”, Zh. Mat. Fiz. Anal. Geom., 13:4 (2017), 325–343
Citation in format AMSBIB
\by K.~Andreiev, I.~Egorova
\paper On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves
\jour Zh. Mat. Fiz. Anal. Geom.
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