Acta Scientific Applied Physics (ASAP)

Research Article Volume 1 Issue 3

Problem of Stability of Solutions of the Generalized Nonlinear Schrödinger Equation in Nonuniform and Nonstationary Media

Vasily Yu Belashov*

Institute of Physics, Kazan Federal University, Kazan, Russia

*Corresponding Author: Vasily Yu Belashov, Institute of Physics, Kazan Federal University, Kazan, Russia.

Received: September 10, 2020; Published: October 30, 2020

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Abstract

  On the basis of the analytical and numerical approaches the stability and dynamics of interaction of the multidimensional soliton-like solutions of the generalized nonlinear Schrödinger equation, which describes the waves in a plasma, fiber and planar optical waveguides, taking into account inhomogeneity and nonstationarity of propagation medium, is studied. The sufficient conditions of stability of the 2-dimensional and 3-dimensional solutions are obtained, and it is shown that even in the simplest 1-dimensional case the GNLS equation can have stable and quasi-stable solutions of the soliton and breather types and also unstable solutions which disperses with time. Obtained results can be useful in numerous applications in plasma physics, nonlinear optics and in many other fields of physics.

Keywords: Generalized Nonlinear Schrödinger Equation; Envelop Solitons; Breathers; Interaction; Multidimensional Solitons; Nonuniform Medium; Nonstationary Medium; Plasma; Fiber; Optical Waveguide

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References

  1. Belashov VYu and Vladimirov SV. “Solitary waves in dispersive complex media”. Theory, simulation, applications. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo (2005).
  2. Belashov VYu., et al. “Problem of stability of multidimensional solutions of the BK class equations in space plasma”. Advances in Space Research 62 (2018): 65-70.
  3. Belashov VYu., et al. “Interaction of the multidimensional NLS solitons in non-uniform and nonstationary medium: modeling and stability problem”. Journal of Astrophysics and Aerospace Technology 6 (2018): 38.
  4. Ginzburg VL and Landau LD. “On the theory of superconductivity”. Journal of Experimental and Theoretical Physics 20 (1950): 1064-1082.
  5. Belashov VYu. “On stability of two-dimensional and three-dimensional solitons in a weakly dispersive media”. DAN SSSR1 (1991): 85-89.
  6. Belashov VYu. “Problem of stability of the three-dimensional Alfvén waves propagating in a magnetized plasma”. Doklady Akademii Nauk 4 (1999): 465-467.
  7. Belashov VYu., et al. “Interaction of multidimensional NLS solitons in nonuniform and nonstationary medium”. 2019 Russian Open Conf. on Radio Wave Prop. (RWP), Kazan, Russia, Kazan Federal University. Proc. IEEE Xplore Digital Library (2019): 535-538.
  8. Belashov VYu., et al. “Dynamics of multidimensional wave structures of the soliton and vortex types in complex continuous media including atmosphere, hydrosphere and space plasma”. 2019 Russian Open Conf. on Radio Wave Prop. (RWP), Kazan, Russia (2019): 19-24.
  9. Belashov VYu and Kharshiladze OA. “Numerical study of evolution and collisional interaction of the GNLS solitons in nonstationary and non-uniform media”. Journal of Lasers, Optics and Photonics 6 (2019): 33-34.
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Citation

Citation: Vasily Yu Belashov. “Problem of Stability of Solutions of the Generalized Nonlinear Schrödinger Equation in Nonuniform and Nonstationary Media". Acta Scientific Applied Physics 1.3 (2020): 01-04.



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