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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

Y. A. Li 1, and  P. J. Olver 1,

1. 

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

Received  December 1996 Revised  January 1997 Published  October 1997

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 and Continuous Dynamical Systems, 1998, 4 (1) : 159-191. doi: 10.3934/dcds.1998.4.159
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