Painlevé-Type Asymptotics for the Camassa-Holm Equation

We consider the initial value problem for the Camassa–Holm equation on the line with decaying initial data. We apply the nonlinear steepest descent approach to compute the long-time asymptotics of the solution in two transition regions. In both regions the asymptotics is expressed in terms of second Painleve transcendents.

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