American Institute of Mathematical Sciences

Advanced
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

M. D. Todorov 1,

1. 

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.
Keywords: Elliptic polarization, Takeover, Collision dynamics, SCNLSE.
Mathematics Subject Classification: Primary: 65M06, 35Q55; Secondary: 35Q51.
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
[1]

Katherine A. Newhall, Gregor Kovačič, Ildar Gabitov. Polarization dynamics in a resonant optical medium with initial coherence between degenerate states. Discrete and Continuous Dynamical Systems - S, 2020, 13 (8) : 2285-2301. doi: 10.3934/dcdss.2020189
[2]

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
[3]

Rong Yang, Li Chen. Mean-field limit for a collision-avoiding flocking system and the time-asymptotic flocking dynamics for the kinetic equation. Kinetic and Related Models, 2014, 7 (2) : 381-400. doi: 10.3934/krm.2014.7.381
[4]

Sergey V. Bolotin. Shadowing chains of collision orbits. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 235-260. doi: 10.3934/dcds.2006.14.235
[5]

Frank Jochmann. Decay of the polarization field in a Maxwell Bloch system. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 663-676. doi: 10.3934/dcds.2003.9.663
[6]

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

Matthias Gerdts, René Henrion, Dietmar Hömberg, Chantal Landry. Path planning and collision avoidance for robots. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 437-463. doi: 10.3934/naco.2012.2.437
[8]

Claudia Totzeck. An anisotropic interaction model with collision avoidance. Kinetic and Related Models, 2020, 13 (6) : 1219-1242. doi: 10.3934/krm.2020044
[9]

Tian Xiang. Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion. Communications on Pure and Applied Analysis, 2019, 18 (1) : 255-284. doi: 10.3934/cpaa.2019014
[10]

King-Yeung Lam, Wei-Ming Ni. Limiting profiles of semilinear elliptic equations with large advection in population dynamics. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1051-1067. doi: 10.3934/dcds.2010.28.1051
[11]

Samuel R. Kaplan, Ernesto A. Lacomba, Jaume Llibre. Symbolic dynamics of the elliptic rectilinear restricted 3--body problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 541-555. doi: 10.3934/dcdss.2008.1.541
[12]

Tatsuki Mori, Kousuke Kuto, Tohru Tsujikawa, Shoji Yotsutani. Exact multiplicity of stationary limiting problems of a cell polarization model. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5627-5655. doi: 10.3934/dcds.2016047
[13]

Gang Bao, Jun Lai. Radar cross section reduction of a cavity in the ground plane: TE polarization. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 419-434. doi: 10.3934/dcdss.2015.8.419
[14]

Alessandro Cucchi, Antoine Mellet, Nicolas Meunier. Self polarization and traveling wave in a model for cell crawling migration. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2381-2407. doi: 10.3934/dcds.2021194
[15]

Adriano Festa, Andrea Tosin, Marie-Therese Wolfram. Kinetic description of collision avoidance in pedestrian crowds by sidestepping. Kinetic and Related Models, 2018, 11 (3) : 491-520. doi: 10.3934/krm.2018022
[16]

Vivina Barutello, Gian Marco Canneori, Susanna Terracini. Minimal collision arcs asymptotic to central configurations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 61-86. doi: 10.3934/dcds.2020218
[17]

Felipe Cucker, Jiu-Gang Dong. A conditional, collision-avoiding, model for swarming. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1009-1020. doi: 10.3934/dcds.2014.34.1009
[18]

Luis A. Caffarelli, Alexis F. Vasseur. The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discrete and Continuous Dynamical Systems - S, 2010, 3 (3) : 409-427. doi: 10.3934/dcdss.2010.3.409
[19]

Tatsuki Mori, Kousuke Kuto, Masaharu Nagayama, Tohru Tsujikawa, Shoji Yotsutani. Global bifurcation sheet and diagrams of wave-pinning in a reaction-diffusion model for cell polarization. Conference Publications, 2015, 2015 (special) : 861-877. doi: 10.3934/proc.2015.0861
[20]

Zhenzhen Zheng, Ching-Shan Chou, Tau-Mu Yi, Qing Nie. Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1135-1168. doi: 10.3934/mbe.2011.8.1135

 Impact Factor: 

Tools

Metrics

  • PDF downloads (57)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy