[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Perturbation Solution to Modified Nonlinear Schr"odinger Equation Based on Slowly Varying Envelope Approximation

Journal of Applied Nonlinear Dynamics 13(2) (2024) 203--210 | DOI:10.5890/JAND.2024.06.002

Arindam Ghosh$^1$, Sarit Maitra$^1$, Asesh Roy Chowdhury$^2$

$^1$ Department of Mathematics, National Institute of Technology Durgapur, India

$^2$ Department of Physics, Jadavpur University, India

Download Full Text PDF

 

Abstract

In this research article a modified nonlinear Schr\"odinger equation describing the dynamics of slowly varying envelope of electromagnetic waves in plasmas is studied. Applying perturbation technique approximate solutions are obtained and plotted numerically. The effects of the physical parameters on the obtained solutions are also examined.

Acknowledgments

The authors are grateful to NIT Durgapur, India for their research support.

References

  1. [1]  Kirkwood, R.K., Moody, J.D., Kline, J., Dewald, E., Glenzer, S., Divol, L., Michel, P., Hinkel, D., Berger, R., Williams, E., and Milovich, J. (2013), A review of laser-plasma interaction physics of indirect-drive fusion, Plasma Physics and Controlled Fusion, 55, 103001.
  2. [2]  Yu, C., Tian, Y., Li, W., Zhang, Z., Qi, R., Wang, W., Wang, C., and Liu, J. (2016), Study of channel formation and relativistic ultra-short laser pulse propagation in helium plasma, Plasma Physics and Controlled Fusion, 58, 055007.
  3. [3]  Amendt, P., Eder, D.C., and Wilks, S.C. (1991), X-ray lasing by optical-field-induced ionization, Physical review letters, 66, 2589.
  4. [4]  Marklund, M. and Shukla, P.K. (2006), Nonlinear collective effects in photon-photon and photon-plasma interactions, Reviews of modern physics, 78, 591.
  5. [5]  Liang, E.P., Wilks, S.C., and Tabak, M. (1998), Pair production by ultraintense lasers, Physical review letters, 81, 4887.
  6. [6]  El-Taibany, W., Karmakar, P., Beshara, A., El-Borie, M., Gwaily, S., and Atteya, A. (2022), Comparison study of the energy and instability of ion-acoustic solitary waves in magnetized electron-positron-ion quantum plasma, Scientific Reports, 12, 19078.
  7. [7]  Guliyev, V.S., Guliyev, R., Omarova, M.N., and Ragusa, M.A. (2020), Schrodinger type operators on local generalized morrey spaces related to certain nonnegative potentials.
  8. [8]  El-Abeda, A., Ali, A.A.B., and Dammak, M. (2022), Schr{\"o}dinger equation with asymptotically linear nonlinearities, Filomat, 36, 629-639.
  9. [9]  Zhang, L., Yang, R., Zhang, L., and Wang, L. (2021), A conservative crank-nicolson fourier spectral method for the space fractional schr{\"o}dinger equation with wave operators, Journal of Function Spaces, 2021, 1-10.
  10. [10]  Amin, M., Morfill, G., and Shukla, P. (1998), Modulational instability of dust-acoustic and dust-ion-acoustic waves, Physical Review E, 58, 6517.
  11. [11]  Peregrine, D.H. (1983), Water waves, nonlinear schr{\"o}dinger equations and their solutions, The ANZIAM Journal, 25, 16-43.
  12. [12]  Javan, N.S. and Adli, F. (2013), Polarization effect on the relativistic nonlinear dynamics of an intense laser beam propagating in a hot magnetoactive plasma, Physical Review E, 88, 043102.
  13. [13]  Crutcher, S.H., Osei, A., and Biswas, A. (2012), Nonlinear evolution equations for surface plasmons for nano-focusing at a kerr/metallic interface and tapered waveguide, Optics $\&$ Laser Technology, 44, 1156-1162.
  14. [14]  Bludov, Y.V., Konotop, V., and Akhmediev, N. (2009), Matter rogue waves, Physical Review A, 80, 033610.
  15. [15]  Maitra, S., Ghosh, A., and Chowdhury, A.R. (2019), Exact solutions and symmetry analysis of a new equation invariant under scaling of dependent variable, Physica Scripta, 94, 085212.
  16. [16]  Ghosh, A., Maitra, S., and Chowdhury, A.R. (2021), Exact solutions and symmetry analysis of a boussinesq type equation for longitudinal waves through a magneto-electro-elastic circular rod, International Journal of Applied and Computational Mathematics, 7, 1-14.
  17. [17]  Ghosh, A. and Maitra, S. (2021), The first integral method and some nonlinear models, Computational and Applied Mathematics, 40, 1-16.
  18. [18]  Malfliet, W. and Hereman, W. (1996), The tanh method: I. exact solutions of nonlinear evolution and wave equations, Physica Scripta, 54, 563.
  19. [19]  Hydon, P.E. and Hydon, P.E. (2000), Symmetry Methods for Differential Equations: a Beginner's Guide, 22, Cambridge University Press.
  20. [20]  Abu~Arqub, O. (2019), Application of residual power series method for the solution of time-fractional schr{\"o}dinger equations in one-dimensional space, Fundamenta Informaticae, 166, 87-110.
  21. [21]  Jaun, A., Hedin, J., and Johnson, T. (1999), Numerical methods for partial differential equations, Swedish Netuniversity.
  22. [22]  Abu~Arqub, O. (2019), Numerical algorithm for the solutions of fractional order systems of dirichlet function types with comparative analysis, Fundamenta Informaticae, 166, 111-137.
  23. [23]  Maayah, B., Arqub, O.A., Alnabulsi, S., and Alsulami, H. (2022), Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the atangana-baleanu-caputo derivative and the reproducing kernel scheme, Chinese Journal of Physics, 80, 463-483.
  24. [24]  Akhmediev, N., Soto-Crespo, J.M., and Ankiewicz, A. (2009), Extreme waves that appear from nowhere: on the nature of rogue waves, Physics Letters A, 373, 2137-2145.
  25. [25]  Xu, S., He, J., and Wang, L. (2011), The darboux transformation of the derivative nonlinear schr{\"o}dinger equation, Journal of Physics A: Mathematical and Theoretical, 44, 305203.
  26. [26]  Zhai, B.-G., Zhang, W.-G., Wang, X.-L., and Zhang, H.-Q. (2013), Multi-rogue waves and rational solutions of the coupled nonlinear schr{\"o}dinger equations, Nonlinear Analysis: Real World Applications, 14, 14-27.
  27. [27]  Yang, B., Zhang, W.-G., Zhang, H.-Q., and Pei, S.-B. (2013), Generalized darboux transformation and rogue wave solutions for the higher-order dispersive nonlinear schr{\"o}dinger equation, Physica Scripta, 88, 065004.
  28. [28]  Luo, Y.-E. and Wang, X.-W. (2020), Modulational instability of ultraintense laser pulses in electron-positron-ion plasmas including vacuum polarization effect, Plasma Physics and Controlled Fusion, 62, 065004.
  29. [29]  Shivamoggi, B.K. (2003), Perturbation Methods for Differential Equations, Springer.
  30. [30]  Rached, Z. (2019), On exact solutions of duffing equation using the modified simple equation method, Global Journal of Pure and Applied Mathematics, 15, 141-145.
  31. [31]  Akbari-Moghanjoughi, M. (2014), Envelope excitations in nonextensive plasmas with warm-ions, Physics Letters A, 378, 3617-3625.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates