This article is cited in 11 papers

The Korteweg-de Vries equation in classes of increasing functions with prescribed asymptotics as $|x|\to\infty$

I. N. Bondareva


Abstract: The Cauchy problem is considered for the Korteweg–de Vries equation with an increasing initial function admitting an asymptotic expansion in decreasing powers of $x$ as $|x|\to\infty$. It is proved that asymptotic solutions having the form of series in decreasing powers of $x$ differ from the actual solutions by a function $w(x,t)$ smooth in $t$ with values in $S(\mathbf R_x)$.
Bibliography: 3 titles.

UDC: 517.9

MSC: 35Q20, 35B20, 65M10

Received: 20.07.1982

 English version: Mathematics of the USSR-Sbornik, 1985, 50:1, 125–135

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