Boussinesq's equation for water waves: Asymptotics in Sector I

Abstract

In a recent study, we showed that the large (x,t)\left(x,t) behavior of a class of physically relevant solutions of Boussinesq’s equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the positive xx-axis, referred to as Sector I, we stated without proof an exact expression for the leading asymptotic term together with an error estimate. Here, we provide a proof of this asymptotic formula.

Keywords

• asymptotics
• boussinesq equation
• riemann-hilbert problem
• initial value problem
• 34e05
• 35g25
• 35q15
• 37k15
• 76b15