Untitled Document SCTP: Saudi Center for Theoretical Physics

 المركز السعودي للفيزياء النظرية
Saudi Center for Theoretical Physics



Academic Year Activities Report 2012-2013


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:


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


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.



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).



Untitled Document SCTP: Saudi Center for Theoretical Physics