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; P. J. Olver

doi:10.3934/dcds.1998.4.159

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1998, Volume 4, Issue 1: 159-191. Doi: 10.3934/dcds.1998.4.159

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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

Received: November 30, 1996

Revised: December 31, 1996

Published: December 1997

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Abstract

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.

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Mathematics Subject Classification: 34A20, 34C35, 35B65, 58F05, 76B25.

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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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