Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system: II. Complex analytic behavior and convergence to non-analytic solutions

In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except for at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support.