Weak solutions of a generalized Boussinesq system
The dynamical systems reduced from the unperturbed and perturbed Boussinesq equations are compared. Four types of weak solutions, including compactons, peakons, rampsons and meseons are shown to be limits of analytic solitary wave solutions of the perturbed system. The solitary wave solutions representing homoclinic orbits or heteroclinic orbits of the perturbed Boussinesq equations are extended to analytic functions defined on some strips in the complex plane, whose boundaries contain singularities as branch points of these functions. These singularities approach the real axis as the corresponding solitary wave solutions converge to any one of the analyzed weak solutions, which is an indication of the strong influence by the nonlinear dispersion terms on the formation of the nonanalytic weak solution.
scientific article; zbMATH DE number 1389696