Long-time limit studies of an obstruction in the g-function mechanism for semiclassical focusing NLS
Publication
, Journal Article
Belov, S; Venakides, S
2015
We consider the long-time properties of the an obstruction in the Riemann-Hilbert approach to one dimensional focusing Nonlinear Schr\"odinger equation in the semiclassical limit for a one parameter family of initial conditions. For certain values of the parameter a large number of solitons in the system interfere with the $g$-function mechanism in the steepest descent to oscillatory Riemann-Hilbert problems. The obstruction prevents the Riemann-Hilbert analysis in a region in $(x,t)$ plane. We obtain the long time asymptotics of the boundary of the region (obstruction curve). As $t\to\infty$ the obstruction curve has a vertical asymptotes $x=\pm \ln 2$. The asymptotic analysis is supported with numerical results.
Duke Scholars
Publication Date
2015
Citation
APA
Chicago
ICMJE
MLA
NLM
Belov, S., & Venakides, S. (2015). Long-time limit studies of an obstruction in the g-function mechanism
for semiclassical focusing NLS.
Belov, S., and S. Venakides. “Long-time limit studies of an obstruction in the g-function mechanism
for semiclassical focusing NLS,” 2015.
Belov S, Venakides S. Long-time limit studies of an obstruction in the g-function mechanism
for semiclassical focusing NLS. 2015;
Belov, S., and S. Venakides. Long-time limit studies of an obstruction in the g-function mechanism
for semiclassical focusing NLS. 2015.
Belov S, Venakides S. Long-time limit studies of an obstruction in the g-function mechanism
for semiclassical focusing NLS. 2015;
Publication Date
2015