Department of Mathematics
University of Missouri
Columbia, MO 65211, USA
email: liyan@missouri.edu
http://faculty.missouri.edu/~liyan
Y. Charles Li
Abstract:
The mechanism of a rogue water wave is still unknown. One popular conjecture
is that the Peregrine wave solution of the nonlinear Schrodinger equation
(NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking
the infinite spatial period limit to the homoclinic solutions.
In this article, from the perspective of the phase space structure of these
homoclinic orbits in the infinite dimensional phase space where the NLS
defines a dynamical system, we examine the observability of these homoclinic
orbits (and their approximations). Our conclusion is that these approximate
homoclinic orbits are the most observable solutions, and they should correspond
to the most common deep ocean waves rather than the rare rogue waves.
We also discuss other possibilities for the mechanism of a rogue wave:
rough dependence on initial data or finite time blow up.
Submitted March 26, 2016. Published April 19, 2016.
Math Subject Classifications: 76B15, 35Q55.
Key Words: Rogue water waves; homoclinic orbits; Peregrine wave;
rough dependence on initial data; finite time blowup.
Show me the PDF file (239 KB), TEX file for this article.
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Y. Charles Li Department of Mathematics University of Missouri Columbia, MO 65211, USA email: liyan@missouri.edu http://faculty.missouri.edu/~liyan |
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