Asymptotic decay of solutions of the Liouville equation under perturbations (Q5930789)

The author considers the Cauchy problem for the perturbed Liouville equation \(\partial^2_t u-\partial^2_xu+8\exp u=\varepsilon (\partial_x F_1(\partial_xu, \partial_tu)+\partial_tF_2(\partial_xu, \partial_tu))\) supplemented with smooth rapidly decaying initial conditions. An asymptotic solution is constructed with respect to the perturbation parameter \(\varepsilon\) by the two-scale expansion method.