2011, 2011(Special): 1385-1394. doi: 10.3934/proc.2011.2011.1385

Polarization dynamics during takeover collisions of solitons in systems of coupled nonlinears Schödinger equations


Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria

Received  July 2010 Revised  April 2011 Published  October 2011

For the system of coupled nonlinear Schrödinger equations we investigate numerically the takeover interaction dynamics of elliptically polarized solitons. In the case of general elliptic polarization, analytical solution for the shapes of a steadily propagating solitons are not available, and we develop a numerical algorithm finding the shape. We use the superposition of generally elliptical polarized solitons as the initial condition for investigating the soliton dynamics. In order to extract the pure effect of the initial phase angle, we consider the case without cross-modulation – the Manakov system. The sum of the masses for the two quasi-particles is constant and the total pseudomementum and energy of the system are conserved. In the case of nontrivial cross-modulation combining it with different initial phase angles causes velocity shifts of interacted solitons. The results of this work outline the role of the initial phase, initial polarization and the interplay between them and nonlinear couplings on the interaction dynamics of solitons in system of coupled nonlinear Schrödinger equations.
Citation: M. D. Todorov. Polarization dynamics during takeover collisions of solitons in systems of coupled nonlinears Schödinger equations. Conference Publications, 2011, 2011 (Special) : 1385-1394. doi: 10.3934/proc.2011.2011.1385

Rong Yang, Li Chen. Mean-field limit for a collision-avoiding flocking system and the time-asymptotic flocking dynamics for the kinetic equation. Kinetic & Related Models, 2014, 7 (2) : 381-400. doi: 10.3934/krm.2014.7.381


M. D. Todorov, C. I. Christov. Collision dynamics of circularly polarized solitons in nonintegrable coupled nonlinear Schrödinger system. Conference Publications, 2009, 2009 (Special) : 780-789. doi: 10.3934/proc.2009.2009.780


Sergey V. Bolotin. Shadowing chains of collision orbits. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 235-260. doi: 10.3934/dcds.2006.14.235


Frank Jochmann. Decay of the polarization field in a Maxwell Bloch system. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 663-676. doi: 10.3934/dcds.2003.9.663


Alfredo Lorenzi. Identification problems related to cylindrical dielectrics **in presence of polarization**. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2247-2265. doi: 10.3934/dcdsb.2014.19.2247


Matthias Gerdts, René Henrion, Dietmar Hömberg, Chantal Landry. Path planning and collision avoidance for robots. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 437-463. doi: 10.3934/naco.2012.2.437


King-Yeung Lam, Wei-Ming Ni. Limiting profiles of semilinear elliptic equations with large advection in population dynamics. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1051-1067. doi: 10.3934/dcds.2010.28.1051


Samuel R. Kaplan, Ernesto A. Lacomba, Jaume Llibre. Symbolic dynamics of the elliptic rectilinear restricted 3--body problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 541-555. doi: 10.3934/dcdss.2008.1.541


Felipe Cucker, Jiu-Gang Dong. A conditional, collision-avoiding, model for swarming. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1009-1020. doi: 10.3934/dcds.2014.34.1009


Adriano Festa, Andrea Tosin, Marie-Therese Wolfram. Kinetic description of collision avoidance in pedestrian crowds by sidestepping. Kinetic & Related Models, 2018, 11 (3) : 491-520. doi: 10.3934/krm.2018022


Gang Bao, Jun Lai. Radar cross section reduction of a cavity in the ground plane: TE polarization. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 419-434. doi: 10.3934/dcdss.2015.8.419


Tatsuki Mori, Kousuke Kuto, Tohru Tsujikawa, Shoji Yotsutani. Exact multiplicity of stationary limiting problems of a cell polarization model. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5627-5655. doi: 10.3934/dcds.2016047


Luis A. Caffarelli, Alexis F. Vasseur. The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 409-427. doi: 10.3934/dcdss.2010.3.409


Yong-Kum Cho. A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem. Kinetic & Related Models, 2012, 5 (3) : 441-458. doi: 10.3934/krm.2012.5.441


Roberto Castelli, Susanna Terracini. On the regularization of the collision solutions of the one-center problem with weak forces. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1197-1218. doi: 10.3934/dcds.2011.31.1197


Pedro J. Torres. Non-collision periodic solutions of forced dynamical systems with weak singularities. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 693-698. doi: 10.3934/dcds.2004.11.693


Cédric Bernardin, Valeria Ricci. A simple particle model for a system of coupled equations with absorbing collision term. Kinetic & Related Models, 2011, 4 (3) : 633-668. doi: 10.3934/krm.2011.4.633


Zhiying Qin, Jichen Yang, Soumitro Banerjee, Guirong Jiang. Border-collision bifurcations in a generalized piecewise linear-power map. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 547-567. doi: 10.3934/dcdsb.2011.16.547


Yong-Kum Cho. On the homogeneous Boltzmann equation with soft-potential collision kernels. Kinetic & Related Models, 2015, 8 (2) : 309-333. doi: 10.3934/krm.2015.8.309


A. V. Bobylev, E. Mossberg. On some properties of linear and linearized Boltzmann collision operators for hard spheres. Kinetic & Related Models, 2008, 1 (4) : 521-555. doi: 10.3934/krm.2008.1.521

 Impact Factor: 


  • PDF downloads (0)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]