Wave propagation and stabilization in the Boussinesq–Burgers system

This paper considers the existence and stability of traveling wave solutions Boussinesq–Burgers system describing propagation bores. Assuming fluid is weakly dispersive, we establish three different profiles by geometric singular perturbation theory alongside phase plane analysis. We further employ method weighted energy estimates to prove nonlinear asymptotic against small perturbations. The technique taking antiderivative utilized integrate functions because conservative structure system. Using a change variable deal with dispersion term, perform numerical simulations for showcase generation various in both weak strong dispersions. not only confirm our analytical results, but also illustrate that can generate numerous propagating depending on initial data intensity dispersion, where particular bores be generated from case dispersion.