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Saudi
Center for Theoretical Physics
Nonlinear
Physics Research Activities
Sept. 2012 to Sept. 2013
I.
Summary
of past and future research progress:
During the
past year we have continued our research
on soliton molecules, exact solutions,
and started two new lines, namely rogue
waves and PT-symmetric potentials.
On soliton
molecules, we have generated two papers,
one paper is published in PRE [1], which
suggests a method of stabilizing the
molecule. The other [7], which explains
the stability of the recent experimental
3-soliton molecules, is submitted to PRA
reports. On exact solutions, we have
completed one paper, [6] and another one
is being worked on, that is submitted.
On rogue
waves, we have generated 2 papers [4,5]
which are both submitted to Phys. Lett.
A. These papers discuss the stability
and controllability of rogue waves.
On
PT-symmetric potentials, we have
published one paper in PRA [3] where a
unidirectional flow is shown to take
place in PT-symmetric potentials. The
new fundamental and applied aspects
associated with this class of
potentials seem to create a trend in
interest. It is therefore, recommended
that we follow up on that work,
especially with our new collaboration
with Yuri Kivshar and collaborators from
the Australian national university (ANU).
So far
collaborations have been established
with 4 international groups:
1.
B.Baizakov
from Physical-Technical Institute, Uzbek
Academy of Sciences Uzbekistan.
Collaboration is mainly on soliton
molecules (theory).
2.
Fedor Mitschke
from Rostock University/Germany.
Collaboration is mainly on soliton
molecules (experimental).
3.
Majid Taki
from Lille university/France.
Collaboration is mainly on rogue waves.
4.
Yuri Kivshar from ANU/Australia.
Collaboration is mainly on PT-symmetric
potentials, Manakov systems, waveguide
arrays, etc.
Future
directions:
We need to
continue work on all research directions
as outlined above and to keep a good
shape for the established
collaborations. Emphasis on some
directions may worth be given, such as
PT-symmetric potentials and rogue waves.
This is motivated by the relatively
larger capacity of the ANU group to host
our collaboration. There are more
members working on fundamental and
trendy topics. It is an active
environment that will help us for
further progress. Furthermore, the
presence of Nail Akhmedeiv, who is in
the field of rogue waves and exact
solutions, at the same place makes it
tempting to strengthen our ties with ANU.
II.
Past and
future research activities:
1.Visits
to KFUPM:
Usama has
conducted the following 3 visits to the
group at KFUPM:
1. Nov.
2012
2. Dec.
2012
3. March
2013
During the
Dec.-visit Abdelaali Boudjumaa from
Algeria was also visiting the group.
During
these visits extensive discussions with
the group members were made. This
resulted in initiating and completing 3
research papers [1,4,7] below. One, with
Yuri Kivshar, being published recently
in PRA and the others are already
submitted.
2.
Nonlinear physics day, Dec. 4, 2012:
A one-day activity with leaders in the
field attending, namely Y. Kivshar and
George Stegeman.
3.
Travel:
1.Conferences
Both Hocine Bahlouli and Usama Al
khawaja have attended the following
relevant conferences. There were many
sessions on rogue waves with leaders in
the field. We benefited greatly from
discussions and obtained insight about
the most important directions for future
work.
·
Conference name:
The Third International Conference
Nonlinear Waves: Theory and
Applications
Place and date:
Beijing, June 12-15, 2013.
Activity:
Attended and presented a talk.
·
Conference name:
International conference in quantum
optics and quantum information
icQoQi
Place and date:
3 - 4 Dec 2013 @ Bukit Gambang Resort
City, Kuantan, Malaysia.
Activity:
Attended and presented a talk.
2.
Visiting ANU/Australia
Usama has
visited the ANU from Aug.14 to sept.6
2013. He collaborated with the
nonlineary physics group of Yuri Kivshar
and some discussions with the group of
Nail akhmediev were also conducted. The
collaboration with the group of Yuri was
mainly on solitons in waveguide arrays
and Bose-Einstein condensation of
polaritons. Both are active topics at
the group. The former being more
relevant to our activities is a
candidate for further follow up. There
are many new ideas that can be followed
up. Here are just few:
1. Soliton
molecules in waveguides.
2.
Unidirectional flow in waveguides.
3. Soliton
transistor.
4.
Future activities:
1.
Nonlinear Physics day at KFUPM
2.
Hosting a visit by Majid Taki Fall 2014.
3.
A
Summer visit to ANU in 2014. It is
recommended that at least 2 members
attend since there are two separate
groups to collaborate with, namely of
Yuri and Akhmediev.
Publications
1) Binding energy of soliton
molecules in time-dependent harmonic
potential and nonlinear interaction
U. Al Khawaja and Abdelali Boudjumaa
Phys. Rev. E 86, 036606 (2012)
Published 20 September 2012.
2) Directional flow of solitons through
asymmetric potentials: a soliton diode
Muhammad Asad Azzaman and U. Al Khawaja,
European Physics letters EPL, 101 (2013)
50008.
3) Unidirectional soliton flows in PT
-symmetric potentials
U. Al Khawaja, S. M. Al-Marzoug, H.
Bahlouli, and Yuri S. Kivshar,
Phys. Rev. A 88, 023830 (2013).
4)Rogue waves management by external
potentials
U. Al Khawaja and M. Taki,
Phys. Lett. A, 377, 2944 (2013).
5)Stability and Dynamics of soliton
molecules in Dispersion-managed Optical
Fibers,
Abdelali Boudjumaa, and U. Al Khawaja,
Phys. Rev. A 88, 045801 (2013).
6)Modulational Instability of the
Peregrine Soliton
U. Al Khawaja, M. Asad-uz-zaman, and S.
M. Al-Marzoug, H. Bahlouli,
Commun Nonlinear Sci Numer Simulat, In
Press (2014).
7)Lax Pairs of higher order nonlinear
Schrödinger equations,
H. Chachou, M. Asad-uz-zaman, and U. Al
Khawaja,
Submitted to Applied Mathematics and
Computation (July 2013).
8)Averaged dynamics of soliton molecules
indispersion-managed optical fibers
S. M. Alamoudi, U. Al Khawaja, and B. B.
Baizakov,
Submitted to Phys Rev. A (2013).
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