Anne Boutet de Monvel, Aleksey Kostenko, Dmitry Shepelsky, Gerald Teschl
Long-Time Asymptotics for the Camassa-Holm Equation
The paper is published: SIAM J. Math. Anal. 41:4 (2009) 1559-1588

MSC:

35B40 Asymptotic behavior of solutions

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07}

58F07 Completely integrable systems (including systems with an infinite number of degrees of freedom)

35B35 Stability, boundedness

58D25 Equations in function spaces; evolution equations, See also {34Gxx, 35K22, 35R15, 47H15}

35Q15 Riemann-Hilbert problems, See also {30E25, 31A25, 31B20}

Abstract: We apply the method of nonlinear steepest descent to compute the long-time
asymptotics of the Camassa--Holm equation for decaying initial data, completing
previous results by A.~Boutet de Monvel and D.~Shepelsky.


Keywords: Camassa--Holm equation, Riemann--Hilbert problem, solitons