THERMAL SCIENCE

International Scientific Journal

Mostafa M. A. Khater

,

Abdel-Haleem Abdel-Aty

,

Ghada Alnemer

,

Mohammed Zakarya

,

Dianchen Lu

NEW OPTICAL EXPLICIT PLETHORA OF THE RESONANT SCHRODINGER'S EQUATION VIA TWO RECENT COMPUTATIONAL SCHEMES

ABSTRACT
This research paper investigates the computational solutions of the resonant Schrödinger's equation. The modified Khater method and Adomian decomposition method are applyied for construct new analytical traveling and semi-analytical wave solutions. This model describes the pulse phenomena and studied in non-linear optics. For further illustration of our obtained solutions, some distinct types of sketches are given.
KEYWORDS
(3+1) resonant Schrodinger’s equation, Modified Khater method, Adomian decomposition method, exact and approximate solutions
PAPER SUBMITTED: 2020-05-11
PAPER REVISED: 2020-06-15
PAPER ACCEPTED: 2020-06-20
PUBLISHED ONLINE: 2020-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI20S1247K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Supplement 1, PAGES [S247 - S255]
REFERENCES
  1. Attia, R. A. M., et al., Optical Wave Solutions of the Higher-Order Non-Linear Schrodinger Equation with the Non-Kerr Non-Linear Term Via Modified Khater Method, Modern Physics Letters B, 34 (2020), 2050044
  2. Ali, A. T., et al., Abundant Numerical and Analytical Solutions of the Generalized Formula of Hirota-Satsuma Coupled KdV System, Chaos, Solitons and Fractals, 131 (2020), 109473
  3. Houwe, A., et al., Chirped Solitons in Discrete Electrical Transmission-Line, Results in Physics, 18 (2020), 103188
  4. Khater, M. M. A., et al., Analytical and Semi-Analytical Ample Solutions of the Higher-Order Non-Linear Schrodinger Equation with the Non-Kerr Non-Linear Term, Results in Physics, 16 (2020), 103000
  5. Khater, M. M. A., et al., On New Computational and Numerical Solutions of the Modified Zakharov-Kuznetsov Equation Arising in Electrical Engineering, Alexandria Engineering Journal, 59 (2020), 3, pp. 1099-1105
  6. Houwe, A., et al., Chirped Solitons in Negative Index Materials Generated in Kerr Non-Linearity, Results in Physics, 17 (2020), 103097
  7. Khater, M. M. A., et al., Analytical and Numerical Solutions for the Current and Voltage Model on an Electrical Transmission-Line with Time and Distance, Physica Scripta, 95 (2020), 055206
  8. Yue, C., et al., Computational Simulations of the Couple Boiti-Leon-Pempinelli (BLP) System and the (3+1)-Dimensional Kadomtsev-Petviashvili (KP) Equation, AIP Advances, 10 (2020), 045216
  9. Houwe, A., et al., Complex Traveling Wave and Soliton Solutions to the Klein-Gordon-Zakharov Equations, Results in Physics, 17 (2020), 103127
  10. Khater, M. M. A., et al., Abundant New Solutions of the Transmission of Nerve Impulses of an Excitable System, The European Physical Journal Plus, 135 (2020), Feb., 251
  11. Abdel-Aty, A.-H., et al., Effect of the Spin-Orbit Interaction on Partial Entangled Quantum Network, Lecture Notes in Electrical Engineering, 285 (2014), 529
  12. Abdel-Aty, A.-H., et al., Quantum Network Via Partial Entangled State, Journal of Communications, 9 (2014), 379
  13. Abdel-Aty, A., et al., Characteristics and Distinctive Features of Entanglement in Superconducting Charge Gubits, Book Title: Quantum Entanglement, Nova Science Publishers Inc., N. Y., USA, 2012, pp. 199-243
  14. Kumar, D., et al., Numerical Simulation for System of Time-Fractional Linear and Non-Linear Differential Equations, Progr. Fract. Differ. Appl., 5 (2019), 1, pp. 65-77
  15. Abdelkawy, M. A., et al., A Spectral Collocation Method for Coupled System of 2-D Abel Integral Equations of the Second Kind, Inf. Sci. Lett., 8 (2019), 3, pp. 89-93
  16. Akram, G., et al., Laguerre Approximations for System of Linear Pantograph Differential Equations, Mathematical Sciences Letters, 7 (2018), Jan., pp. 125-131
  17. Qian, L., et al., On Breather and Cuspon Waves Solutions for the Generalized Higher-Order Non-Linear Schrodinger Equation with Light-Wave Promulgation in an Optical Fiber, Num. Comp. Meth. Sci. Eng, 1 (2019), 2, pp. 101-110
  18. Cherniha, R., et al., Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis, Symmetry, 8 (2016), 50
  19. Khater, M. M. A., et al., Dispersive Long Wave of Non-Linear Fractional Wu-Zhang System Via a Modified Auxiliary Equation Method, AIP Advances, 9 (2019), 025003
  20. Osman, M. S., et al., A Study of Optical Wave Propagation in the Non-Autonomous Schrodinger-Hirota Equation with Power-Law Non-Linearity, Results in Physics, 13 (2019), 102157
  21. Attia, R. A. M., et al., Chaos and Relativistic Energy-Momentum of the Non-Linear Time Fractional Duffing Equation, Mathematical and Computational Applications, 24 (2019), 10
  22. Khater, M. M. A., et al., Lump Soliton Wave Solutions for the (2+1)-Dimensional Konopelchenko-Dubrovsky Equation and KdV Equation, Modern Physics Letters B, 33 (2019), 1950199
  23. Benslimane, A., et al., Displacements and Stresses in Pressurized Thick-Walled FGM Cylinders: Exact and Numerical Solutions, International Journal of Pressure Vessels and Piping, 168 (2018), Dec., pp. 219-224
  24. Guo, P., Chong-Jun, L., Almost Sure Stability with General Decay Rate of Exact and Numerical Solutions for Stochastic Pantograph Differential Equations, Numerical Algorithms, 80 (2019), 2, pp. 1391-1411
  25. Euler, M., Euler, N., On Mobius‐Invariant and Symmetry‐Integrable Evolution Equations and the Schwarzian Derivative, Studies in Applied Mathematics, 143 (2019), 2, pp. 139-156
  26. Attia, R. A., et al., Structure of New Solitary Solutions for the Schwarzian Korteweg De Vries Equation and (2+1)-Ablowitz-Kaup-Newell-Segur Equation, Phys. J, 1 (2018), 3, pp. 234-254
  27. Inc, M., On Numerical Doubly Periodic Wave Solutions of the Coupled Drienfel'd-Sokolov-Wilson Equation by the Decomposition Method, Appl. Math. Comput., 172 (2006), 1, pp. 421-430
  28. Inc, M., On Numerical Jacobi Elliptic Function Solutions of the (1+1)-Dimensional Dispersive Long Wave Equation by the Decomposition Method, Appl. Math. Comput., 173 (2006), 1, pp. 372-382
  29. Inc, M., Exact Solutions with Solitary Patterns for the Zakharov-Kuznetsov Equations with Fully Non-Linear Dispersion, Chaos, Solitons and Fractals, 33 (2007), 5, pp. 1783-1790
  30. Xue, G., et al., Darboux Transformation for a Generalized Ablowitz-Kaup-Newell-Segur Hierarchy Equation, Physics Letters A, 384 (2020), 126394
  31. Hosseini, K., et al., A (3+1)-Dimensional Resonant Non-Linear Schrodinger Equation and Its Jacobi Elliptic and Exponential Function Solutions, Optik, 207 (2020), 164458
  32. Korpinar, Z., et al., Newoptical Solitons for Biswas-Arshed Equation with Higher Order Dispersions and Fully Non-Linearity, Optik, 206 (2020), 163332
  33. Inc, M., et al., Optical Solitons to the Resonance Non-Linear Schrodinger Equation by Sine-Gordon Equation Method, Superlattices and Microstructures, 113 (2018), Jan., pp. 541-549
  34. Aslan, E. C., Inc, M., Optical Soliton Soluions of the NLSE Quadratic-Cubic-Hamiltonian Perturbations and Modulation Instability Analysis, Optik, 196 (2019), 162661
  35. Inc, M., et al., Optical Solitons and Modulation Instability Analysis of (3+1)-Dimensional Non-Linear Schrodinger Equation, Superlattices and Microstructures, 112 (2017), Sept., pp. 296-302
  36. Golmankhaneh, A. K., et al., A Review on Local and Non-Local Fractal Calculus, Num. Com. Meth. Sci. Eng., 1 (2019), Jan., pp. 19-31
  37. Taiwo, T. J., et al., Four-Parameter Potential Function with Negative Energy Bound States, Inf. Sci. Lett., 8 (2019), 1, pp. 25-31
  38. Tsega, E. G., A Finite Volume Solution of Unsteady Incompressible Navier-Stokes Equations Using MATLAB, Num. Com. Meth. Sci. Eng., 1 (2019), 117
  39. Al-Saif, A. S. J., Abdul-Wahab M. S., Application of New Simulation Scheme for the Non-Linear Biological Population Model, Num. Com. Meth. Sci. Eng., 1 (2019), 89
  40. Tasbozan, O., et al., New Analytical Solutions and Approximate Solution of the Space-Time Conformable Sharma-Tasso-Olver Equation, Progr. Fract. Differ. Appl., 4 (2018), Jan., pp. 519-531
  41. Khater, M. M. A., et al., Computational Analysis of a Non-Linear Fractional Emerging Telecommunication Model with Higher-order Dispersive Cubic-Quintic, Inf. Sci. Lett., 9 (2020), 2, pp. 83-93
  42. Wazwaz, A., A Reliable Modification of Adomian Decomposition Method, Applied Mathematics and Computation, 102 (1999), 1, pp. 77-86
  43. Li, W., Pang, Y. Application of Adomian Decomposition Method to Non-Linear Systems, Adv. Differ Equ., 2020 (2020), 67
  44. Kulkarni, S., et.al., Application of Adomian Decomposition Method to Solve the Fractional Mathematical Model of Corona Virus, Journal Math. Comput. Sci., 10 (2020), 5, pp. 1327-1339
PDF VERSION [DOWNLOAD]
New optical explicit plethora of the resonant Schrodinger's equation via two recent computational schemes

© 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