| Abstract: | Some recent results in the asymptotic theory of differential equations are applied to certain third-order scalar and vector boundary-value problems that model various nonlinear physicochemical and dispersive wave phenomena. The key to our approach is the reduction of the third-order problems to asymptotically equivalent second-order ones which are more amenable to analysis. Many examples are discussed, including the problem of solitary-wave solutions of generalized Korteweg-de Vries equations and coupled systems of such equations. |
