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| Publications [#320540] of Stephanos Venakides
Papers Published
- Belov, S; Venakides, S, Long-time limit studies of an obstruction in the g-function mechanism
for semiclassical focusing NLS
(2015)
(last updated on 2026/01/13)
Abstract:
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.
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