Boussinesq's equation for water waves: asymptotics in sector I (Q6580487)

The authors in a previous paper [``On Boussinesqas equation for water waves'', Preprint, \url{arXiv:2204.02365}] developed an inverse scattering approach to the Boussinesq equation, which yields an expression for the solution $u(x,t)$ in terms of the solution $n(x,t,k)$ of a $1\times 3$-row-vector Riemann-Hilbert (RH) problem. In this paper, the authors derive an exact expression for the leading asymptotic term together with an error estimate for the large $(x,t)$ behavior of $u(x,t)$ in the sector adjacent to the positive $x$-axis, referred to as Sector I.