The "good'' Boussinesq equation: long-time asymptotics

Abstract

We consider the initial-value problem for the ``good'' Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a $3\times 3$-matrix Riemann-Hilbert problem. We establish formulas for the long-time asymptotics of the solution by performing a Deift-Zhou steepest descent analysis of a regularized version of this Riemann-Hilbert problem.

34 pages, 13 figures

References in corpus (2)

• Long-Time Asymptotics for the Camassa-Holm Equation
• Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation

Cited by in corpus (3)

• Long-time asymptotics for an integrable evolution equation with a $3\times 3$ Lax pair
• Long-time asymptotics of the Tzitzéica equation on the line
• Asymptotic Properties of a Special Solution to the (3,4) String Equation