American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 780-789. doi: 10.3934/proc.2009.2009.780

Collision dynamics of circularly polarized solitons in nonintegrable coupled nonlinear Schrödinger system

M. D. Todorov 1, and  C. I. Christov 2,

1. 

Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria
2. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States

Received  August 2008 Revised  March 2009 Published  September 2009

The system of Coupled Nonlinear Schrödinger Equations (CNLSEs) is solved by a conservative difference scheme in complex arithmetic developed in earlier author's work. The initial condition represents a superposition of two one-soliton solutions of different circular polarizations. The interaction (collision) of the solitons and their quasi-particle (QP) behavior is examined for different configurations of the initial system of QPs. We found that the polarization angle of a QP can change after a collision with another QP depending on the configuration of the initial phases. The effects found in the present work seem to be novel and enrich the knowledge about the intimate mechanisms of interaction of polarized QPs of CNLSEs.
Keywords: Collision dynamics, Elliptic polarization, Quasi-particles, Conservative numerical schemes.
Mathematics Subject Classification: Primary: 65M06, 35Q55; Secondary: 35Q51.
Citation: 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
[1]

Corrado Falcolini, Laura Tedeschini-Lalli. A numerical renormalization method for quasi–conservative periodic attractors. Journal of Computational Dynamics, 2020, 7 (2) : 461-468. doi: 10.3934/jcd.2020018
[2]

Patrick Henning, Johan Wärnegård. Numerical comparison of mass-conservative schemes for the Gross-Pitaevskii equation. Kinetic and Related Models, 2019, 12 (6) : 1247-1271. doi: 10.3934/krm.2019048
[3]

Anaïs Crestetto, Nicolas Crouseilles, Mohammed Lemou. Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles. Kinetic and Related Models, 2012, 5 (4) : 787-816. doi: 10.3934/krm.2012.5.787
[4]

Marx Chhay, Aziz Hamdouni. On the accuracy of invariant numerical schemes. Communications on Pure and Applied Analysis, 2011, 10 (2) : 761-783. doi: 10.3934/cpaa.2011.10.761
[5]

Gianluca Frasca-Caccia, Peter E. Hydon. Locally conservative finite difference schemes for the modified KdV equation. Journal of Computational Dynamics, 2019, 6 (2) : 307-323. doi: 10.3934/jcd.2019015
[6]

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
[7]

Mark Wilkinson. A Lie algebra-theoretic approach to characterisation of collision invariants of the Boltzmann equation for general convex particles. Kinetic and Related Models, 2022, 15 (2) : 283-315. doi: 10.3934/krm.2022008
[8]

Filippo Gazzola, Lorenzo Pisani. Remarks on quasilinear elliptic equations as models for elementary particles. Conference Publications, 2003, 2003 (Special) : 336-341. doi: 10.3934/proc.2003.2003.336
[9]

P. Smoczynski, Mohamed Aly Tawhid. Two numerical schemes for general variational inequalities. Journal of Industrial and Management Optimization, 2008, 4 (2) : 393-406. doi: 10.3934/jimo.2008.4.393
[10]

Samira Amraoui, Didier Auroux, Jacques Blum, Emmanuel Cosme. Back-and-forth nudging for the quasi-geostrophic ocean dynamics with altimetry: Theoretical convergence study and numerical experiments with the future SWOT observations. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022058
[11]

M. D. Todorov, C. I. Christov. Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations. Conference Publications, 2007, 2007 (Special) : 982-992. doi: 10.3934/proc.2007.2007.982
[12]

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
[13]

Hyeong-Ohk Bae, Young-Pil Choi, Seung-Yeal Ha, Moon-Jin Kang. Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4419-4458. doi: 10.3934/dcds.2014.34.4419
[14]

Douglas Hardin, Edward B. Saff, Ruiwen Shu, Eitan Tadmor. Dynamics of particles on a curve with pairwise hyper-singular repulsion. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5509-5536. doi: 10.3934/dcds.2021086
[15]

Nikolaos Halidias. Construction of positivity preserving numerical schemes for some multidimensional stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 153-160. doi: 10.3934/dcdsb.2015.20.153
[16]

Hélène Hivert. Numerical schemes for kinetic equation with diffusion limit and anomalous time scale. Kinetic and Related Models, 2018, 11 (2) : 409-439. doi: 10.3934/krm.2018019
[17]

Corrado Falcolini, Laura Tedeschini-Lalli. Diverging period and vanishing dissipation: Families of periodic sinks in the quasi-conservative case. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6105-6122. doi: 10.3934/dcds.2018263
[18]

Gennadiy Burlak, Salomon García-Paredes. Matter-wave solitons with a minimal number of particles in a time-modulated quasi-periodic potential. Conference Publications, 2015, 2015 (special) : 169-175. doi: 10.3934/proc.2015.0169
[19]

Yusuke Murase, Risei Kano, Nobuyuki Kenmochi. Elliptic Quasi-variational inequalities and applications. Conference Publications, 2009, 2009 (Special) : 583-591. doi: 10.3934/proc.2009.2009.583
[20]

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

 Impact Factor: 

Tools

Metrics

  • PDF downloads (59)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy