Nonlinear non-autonomous Boussinesq equations

We study solitary wave solutions for a nonlinear and non-autonomous Boussinesq system with initial conditions. Since the variable coefficients introduce distortions and modulations of the solution amplitudes, we implement a multiple-scale approach combining various modes in order to capture the coupling between the nonlinear evolution and the effect of the variable coefficient. The differential system is mapped into a solvable system of nonlinear and non-autonomous ODE which is integrable by recursion procedures. We show that even in the limiting autonomous case, the multiple-scale approach gives a new possibly integrable dispersionless coupled envelope system, which deserves further study. We validate our theoretical results with numerical simulations, and we study their stability. For more information see https://ejde.math.txstate.edu/conf-proc/27/l1/abstr.html