Science and Mathematics Faculty Publications
Bounded Ultra-elliptic Solutions of the Defocusing Nonlinear Schrödinger Equation
Document Type
Article
Publication Date
12-2017
Journal Title
Physica D: Nonlinear Phenomena
ISSN
0167-2789
Volume
360
First Page
1
Last Page
16
DOI
https://doi.org/10.1016/j.physd.2017.08.013
Abstract
An effective integration method is presented for the bounded ultra-elliptic solutions of the defocusing nonlinear Schrödinger equation. The two-phase solutions are explicitly parametrized in terms of two physically-meaningful variables: the energy density and the momentum density. Cavitation, viz., a minimum amplitude of zero, occurs if and only if the length of the largest spectral band is less than or equal to the sum of the lengths of the two smaller spectral bands. In the case of strict inequality, there are exactly two cavitation points in each period parallelogram.
Keywords
Nonlinear Schrödinger equation, two-phase solutions, Cavitation
Recommended Citation
Wright, Otis C. III, "Bounded Ultra-elliptic Solutions of the Defocusing Nonlinear Schrödinger Equation" (2017). Science and Mathematics Faculty Publications. 360.
https://digitalcommons.cedarville.edu/science_and_mathematics_publications/360
