Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions

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January 1998, 4(1): 159-191. doi: 10.3934/dcds.1998.4.159

Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions

1.	School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States

Received December 1996 Revised January 1997 Published October 1997

Abstract
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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.

Keywords: Solitary-wave solutions, bi-Hamiltonian dynamical system, complex analytic behavior..

Mathematics Subject Classification: 34A20, 34C35, 35B65, 58F05, 76B2.

Citation: Y. A. Li, P. J. Olver. Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 159-191. doi: 10.3934/dcds.1998.4.159

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