THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

THE EXACT SOLUTION OF THE NON-LINEAR SCHRODINGER EQUATION BY THE EXP-FUNCTION METHOD

ABSTRACT
This paper elucidates the main advantages of the exp-function method in finding the exact solution of the non-linear Schrodinger equation. The solution process is extremely simple and accessible, and the obtained solution contains some free parameters.
KEYWORDS
PAPER SUBMITTED: 2020-03-01
PAPER REVISED: 2020-06-01
PAPER ACCEPTED: 2020-06-01
PUBLISHED ONLINE: 2021-03-27
DOI REFERENCE: https://doi.org/10.2298/TSCI200301088C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2057 - 2062]
REFERENCES
  1. Hi, A. G., et al., Optical Solitons and Stability Analysis with Coupled Non-linear Schrodinger's Equations Having Double External Potentials, Results in Physics, 15 (2019), Dec., ID 102707
  2. Adebimpe, O., et al., Bound State Solutions of the Schrodinger Equation and Expectation Value for Some Molecules, Results in Physics, 15 (2019), Dec., ID 102769
  3. Ali, I., et al., Optical Solitons for Modulated Compressional Dispersive Alfven and Heisenberg Ferromagnetic Spin Chains, Results in Physics, 15 (2019), Dec., ID 102714
  4. Du, S. Y., Optical Solitons and Envelop Propagation Patterns in Birefringent Polarization-Preserving Fiber, Results in Physics, 15 (2019), Dec., ID 102795
  5. Hafez, M. G., et al., Oblique Plane Waves with Bifurcation Behaviors and Chaotic Motion for Resonant Non-Linear Schrodinger Equations Having Fractional Temporal Evolution, Results in Physics, 15 (2019), Dec., ID 102778
  6. He, J. R., et al., Non-linear Tunneling Effect of Snakelike Self-Similar Waves in a Grating Dual-Core Waveguide Amplifier, Results in Physics, 15 (2019), Dec., ID 102742
  7. Nasreen, N., et al., Dispersive Solitary Wave and Soliton Solutions of the Generalized Third Order Non-linear Schrodinger Dynamical Equation by Modified Analytical Method, Results in Physics, 15 (2019), Dec., ID 102641
  8. Yang, X. Y., et al., Periodic Propagation of Radially and Azimuthally Polarized First-Order Chirped Airy Gaussian Beams in a Harmonic Potential, Results in Physics, 15 (2019), Dec., ID 102691
  9. He, J. H., Variational Principle and Periodic Solution of the Kundu-Mukherjee-Naskar Equation, Results in Physics, 17 (2020), June, ID 103031
  10. Anjum, N., He, J. H., Laplace Transform: Making the Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138
  11. He, J. H., Latifizadeh, H., A General Numerical Algorithm for Non-linear Differential Equations by the Variational Iteration Method, International Journal of Numerical Methods for Heat and Fluid Flow, 30 (2020), 11, pp. 4797-4810
  12. Wu, Y., He, J. H., Homotopy Perturbation Method for Non-linear Oscillators with Coordinate Dependent Mass. Results in Physics, 10 (2018), Sept., pp. 270-271
  13. Yu, D. N., et al., Homotopy Perturbation Method with an Auxiliary Parameter for Non-linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1540-1554
  14. He, J. H., Generalized Variational Principles for Buckling Analysis of Circular Cylinders, Acta Mechanica, 231 (2020), 3, pp. 899-906
  15. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  16. He, J. H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: From Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
  17. He, J. H., A Short Review on Analytical Methods for to a Fully Fourth-Order Non-linear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid Flow, 30 (2020), 11, pp. 4933-4943
  18. He, J. H., Jin, X., A Short Review on Analytical Methods for the Capillary Oscillator in a Nanoscale Deformable Tube, Mathematical Methods in the Applied Sciences, On-line first, dx.doi.org/10.1002/ mma.6321, 2020
  19. He, J. H., The Simpler, the Better: Analytical Methods for Non-linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1252-1260
  20. He, C. H., et al., Fangzhu, An Ancient Chinese Nanotechnology for Water Collection from Air: History, Mathematical Insight, Promises and Challenges, Mathematical Methods in the Applied Sciences, On-line first, doi.org/10.1002/mma.6384, 2020
  21. He, J. H., Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012 (2012), ID 916793
  22. Kohl, R. W., et al., Cubic-Quartic Optical Soliton Perturbation by Semi-Inverse Variational Principle. Optik - International Journal for Light and Electron Optics, 185 (2019), May, pp. 45-49
  23. He, J. H., Wu, X. H., Exp-Function Method for Non-linear Wave Equations, Chaos Solitons & Fractals, 30 (2006), 3, pp. 700-708
  24. He, J. H., Exp-Function Method for Fractional Differential Equations, International Journal of Non-linear Sciences and Numerical simulation, 14 (2013), 6, pp. 363-366
  25. He, J. H., Zhang, L. N., Generalized Solitary Solution and Compacton-Like Solution of the Jaulent-Miodek Equations Using the Exp-Function Method, Phys. Lett. A. 372 (2008), 7, pp. 1044-1047
  26. Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448
  27. Jia, Z. J., et al., Local Fractional Differential Equations by the Exp-Function Method, International Journal of Numerical Methods for Heat and Fluid Flow, 25 (2015), 8, pp. 1845-1849
  28. He, J. H., et al., Difference Equation vs. Differential Equation on Different Scales, International Journal of Numerical Methods for Heat and Fluid Flow, 31 (2020), 1, pp. 391-401

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence