Optical solitons for conformable space-time fractional nonlinear model
Volume 27, Issue 1, pp 28--41
http://dx.doi.org/10.22436/jmcs.027.01.03
Publication Date: February 10, 2022
Submission Date: September 08, 2021
Revision Date: November 07, 2021
Accteptance Date: December 02, 2021
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Authors
M. I. Asjad
- Department of Mathematics, University of Management and Technology, Lahore, Pakistan.
N. Ullah
- Department of Mathematics, University of Management and Technology, Lahore, Pakistan.
H. u. Rehman
- Department of Mathematics, University of Okara, Okara, Pakistan.
D. Baleanu
- Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey.
- Institute of Space Sciences, R76900 Magurele-Bucharest, Romania.
Abstract
In search of the exact solutions of nonlinear partial differential
equations
in solitons form has become most popular to understand the internal features
of physical phenomena. In this paper, we discovered various type of solitons
solutions for the conformable space-time nonlinear Schrodinger equation (CSTNLSE)
with Kerr law nonlinearity. To seek such solutions, we applied two proposed methods
which are Sardar-subequation method and new extended hyperbolic function method.
In this way several types of solitons obtained for example bright, dark, periodic
singular, combined dark-bright, singular, and combined singular solitons.
Some of the acquired solutions are interpreted
graphically. These solutions are
specific, novel, correct and may be beneficial for edifying precise
nonlinear physical phenomena in nonlinear dynamical schemes. It is
revealed that the proposed methods offer a straightforward and
mathematical tool for solving nonlinear conformable space-time
nonlinear Schrodinger equation. These results support in attaining nonlinear optical fibers in the future.
Share and Cite
ISRP Style
M. I. Asjad, N. Ullah, H. u. Rehman, D. Baleanu, Optical solitons for conformable space-time fractional nonlinear model, Journal of Mathematics and Computer Science, 27 (2022), no. 1, 28--41
AMA Style
Asjad M. I., Ullah N., Rehman H. u., Baleanu D., Optical solitons for conformable space-time fractional nonlinear model. J Math Comput SCI-JM. (2022); 27(1):28--41
Chicago/Turabian Style
Asjad, M. I., Ullah, N., Rehman, H. u., Baleanu, D.. "Optical solitons for conformable space-time fractional nonlinear model." Journal of Mathematics and Computer Science, 27, no. 1 (2022): 28--41
Keywords
- Sardar-subequation method
- conformable space-time nonlinear Schrodinger equation
- the new extended hyperbolic function method
- optical solitons
MSC
References
-
[1]
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57--66
-
[2]
M. Abu Hammad, R. Khalil, Conformable fractional heat differential equation, Int. J. Pure Appl. Math., 94 (2014), 215--221
-
[3]
A. Akgül, A novel method for a fractional derivative with non-local and non-singular kernel, Chaos Soliton Fractal, 114 (2018), 478--482
-
[4]
M. Arshad, A. R. Seadawy, D. Lu, Bright–dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics, J. Electromagnet Waves Appl., 31 (2017), 1711--1721
-
[5]
D. Baleanu, A. Fernandez, A. Akgül, On a fractional operator combining proportional and classical differintegrals, Mathematics, 8 (2020), 13 pages
-
[6]
D. Baleanu, M. Inc, A. Yusuf, A. I. Aliyu, Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov-Kuznetsov equation, Nonlinear Anal. Model. Control, 22 (2017), 861--876
-
[7]
D. Baleanu, M. Inc, A. Yusuf, A. I. Aliyu, Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation, Commun. Nonlinear Sci. Numer. Simulat., 59 (2018), 222--234
-
[8]
D. Baleanu, M. Inc, A. Yusuf, A. I. Aliyu, Time fractional third-order evolution equation: symmetry analysis, explicit solutions, and conservation laws, J. Comput. Nonlinear Dyn., 13 (2018), 021011-5
-
[9]
A. Biswas, Soliton solutions of the perturbed resonant nonlinear Schrödinger equation with full nonlinearity by semi-inverse variational principle, Quantum Phys. Lett., 1 (2012), 79--89
-
[10]
A. Biswas, M. O. AlAmr, H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, Resonant optical solitons with dual-power law nonlinearity and fractional temporal evolution, Optik, 165 (2018), 233--239
-
[11]
A. Biswas, M. Mirzazadeh, M. Eslami, D. Milovic, Solitons in optical metamaterials by functional variable method and first integral approach, Frequenz, 68 (2014), 525--530
-
[12]
A. Biswas, R. Morris, A. H. Kara, Soliton solution and conservation laws of the Zakharov-Kuznetsov equation in plasmas with power law nonlinearity, Nonlinear Anal. Model. Control, 18 (2013), 153--159
-
[13]
M. Ekici, M. Mirzazadeh, M. Eslami, Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion, Nonlinear Dyn., 84 (2016), 669--676
-
[14]
M. Ekici, M. Mirzazadeh, M. Eslami, Q. Zhou, S. P. Moshokoa, A. Biswas, M. Belic, Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127 (2016), 10659--10669
-
[15]
M. Eslami, Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Appl. Math. Comput., 285 (2016), 141--148
-
[16]
M. Eslami, Trial solution technique to chiral nonlinear Schrodinger equation in $(1+2)$-dimensions, Nonlinear Dyn., 85 (2016), 813--816
-
[17]
M. Eslami, F. S. Khodadad, F. Nazari, H. Rezazadeh, The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative, Opt. Quant. Electron., 49 (2017), 18 pages
-
[18]
M. Eslami, M. Mirzazadeh, Optical solitons with Biswas-Milovic equation for power law and dual-power law nonlinearities, Nonlinear Dyn., 83 (2016), 731--738
-
[19]
M. Eslami, A. Neirameh, New exact solutions for higher order nonlinear Schrödinger equation in optical fibers, Opt. Quant. Electron., 50 (2017), 8 pages
-
[20]
M. Eslami, H. Rezazadeh, The first integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53 (2016), 475--485
-
[21]
Commun. Nonlinear Sci. Numer. Simul., Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations, 2014, 153--163 (23),
-
[22]
M. S. Hashemi, Group analysis and exact solutions of the time fractional Fokker-Planck equation, Phys. A Stat. Mech. Appl., 417 (2015), 141--149
-
[23]
M. S. Hashemi, A. Akgül, Solitary wave solutions of time-space nonlinear fractional Schrödinger's equation: two analytical approaches, J. Comput. Appl. Math., 339 (2017), 147--160
-
[24]
M. S. Hashemi, M. Inc, B. Kilic, A. Akgül, On solitons and invariant solutions of the Magneto-electro-elastic circular rod, Waves in Random and Complex Media, 26 (2016), 259--271
-
[25]
K. Hosseini, R. Ansari, New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method, Waves Random Complex Media, 27 (2017), 628--636
-
[26]
K. Hosseini, A. Bekir, R. Ansari, New exact solutions of the conformable time-fractional Cahn-Allen and Cahn-Hilliard equations using the modified Kudryashov method, Optik, 132 (2017), 203--209
-
[27]
K. Hosseini, A. Bekir, M. Kaplan, Ö. Güner, A new technique for solving the nonlinear conformable time-fractional differential equations, Opt. Quant. Electron., 49 (2017), 12 pages
-
[28]
K. Hosseini, P. Mayeli, R. Ansari, Bright and singular soliton solutions of the conformable time-fractional Klein-Gordon equations with different nonlinearities, Waves Random Complex Media, 28 (2017), 426--434
-
[29]
K. Hosseini, P. Mayeli, A. Bekir, O. Guner, Density-dependent conformable space-time fractional diffusion-reaction equation and its exact solutions, Commun. Thoer. Phys., 69 (2018), 4 pages
-
[30]
K. Hosseini, Y. J. Xu, P. Mayeli, A. Bekir, P. Yao, Q. Zhou, O. Guner, A study on the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities, Optoelectron. Adv. Mater. Rapid Commun., 11 (2017), 423--429
-
[31]
A. Houwe, M. B. Hubert, S. Nestor, D. Jerome, M. Justin, G. Betchewe, S. Y. Doka, K. T. Crepin, S. Khan, A. Biswas, M. Ekici, S. Adesanya, S. P. Moshokoa, M. Belic, Optical solitons for higher-order nonlinear Schrödinger equation with three exotic integration architectures, Optik, 17 (2019), 861--866
-
[32]
M. Inc, A. Akgül, Classifications of Soliton Solutions of the Generalized Benjamin-Bona-Mahony Equation with Power-Law Nonlinearity, J. Adv. Phys., 7 (2018), 130--134
-
[33]
M. Inc, I. A. Aliyu, A. Yusuf, D. Baleanu, Dispersive optical solitons and modulation instability analysis of Schrodinger-Hirota equation with spatio-temporal dispersion and Kerr law nonlinearity, Superlattices Microstruct, 113 (2018), 319--327
-
[34]
M. Inc, A. Yusuf, A. I. Aliyu, D. Baleanu, Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: lie symmetry analysis, explicit solutions and convergence analysis, Phys. A, 493 (2018), 94--106
-
[35]
R. Khalil, A. L. M. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65--70
-
[36]
F. S. Khodadad, F. Nazari, M. Eslami, H. Rezazadeh, Soliton solutions of the conformable fractional Zakharov-Kuznetsov equation with dual-power law nonlinearit, Opt. Quant. Electron., 49 (2017), 384
-
[37]
A. Korkmaz, K. Hosseini, Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable method, Opt. Quant. Electron., 49 (2017), 10 pages
-
[38]
S. Y. Lukashchuk, Conservation laws for time-fractional sub-diffusion and diffusion-wave equations, Nonlinear Dyn., 80 (2015), 791--802
-
[39]
M. Mirzazadeh, M. Eslami, A. Biswas, $1$--Soliton solution of KdV6 equation, Nonlinear Dyn., 80 (2015), 387--396
-
[40]
M. Mirzazadeh, M. Eslami, B. F. Vajargah, A. Biswas, Application of the first integral method to fractional partial differential equations, Indian J. Phys., 88 (2014), 177--184
-
[41]
A. Neirameh, M. Eslami, An analytical method for finding exact solitary wave solutions of the coupled $(2+1)$-dimensional Painleve Burgers equation, Sci. Iran., 24 (2017), 715--726
-
[42]
S. Nestor, A. Houwe, G. Betchewe, M. Inc, S. Y. Doka, A series of abundant new optical solitons to the conformable space-time fractional perturbed nonlinear Schrödinger equation, Physica Scripta, 95 (2020), 11 pages
-
[43]
H. U. Rehman, M. A. Imran, M. Bibi, A. Akgül, New soliton solutions of the 2D-chiral nonlinear Schrodinger equation using two integration schemes, Math. Methods Appl. Sci., 44 (2021), 5663--5682
-
[44]
H. Rezazadeh, M. Inc, D. Baleanu, New Solitary Wave Solutions For Variants Of $(3+1)$-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations, Frontiers Phys., 8 (2020), 12 pages
-
[45]
Y. Shang, The extended hyperbolic function method and exact solutions of the long-short wave resonance equations, Chaos Solitons Fractals, 36 (2008), 762--771
-
[46]
Y. Shang, Y. Huang, W. Yuan, The extended hyperbolic functions method and new exact solutions to the Zakharov equations, Appl. Math. Comput., 200 (2008), 110--122
-
[47]
A. Sonomezoglu, M. Eslami, Q. Zhou, E. Zerrad, A. Biswas, M. Belic, M. Mirzazadeh, M. Ekici, Optical solitons in nano-fibers with fractional temporal evolution, J. Comput. Theor. Nanosci., 13 (2016), 5361--5374
-
[48]
A. Sonomezoglu, S. Ortakaya, M. Eslami, A. Biswas, M. Mirzazadeh, M. Ekici, Solitons solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics, Eur. Phys. J. Plus, 131 (2016), 166--177
-
[49]
P. Suarez, A. Biswas, Exact 1-soliton solution of the Zakharov equation in plasmas with power law nonlinearity, Appl. Math. Comput., 217 (2011), 7372--7375
-
[50]
F. Tchier, M. Inc, B. Kilic, A. Akgül, On soliton structures of generalized resonance equation with time dependent coefficients, Optik, 128 (2017), 218--223
-
[51]
B. F. Vajargah, M. Mirzazadeh, M. Eslami, A. Biswas, Solitons and periodic solutions to a couple of fractional nonlinear evolution equations, Pramana, 82 (2014), 465--476
-
[52]
E. Zerrad, A. Biswas, R. Kohl, D. Milovic, Optical solitons by He's variational principle in a non-Kerr law media, J. Infrared Millim. Terahertz Waves, 30 (2009), 526--537
-
[53]
E. Zerrad, A. Biswas, M. Song, B. Ahmed, Domain wall and bifurcation analysis of the klein-gordon Zakharov-Kuznetsov equation in $(1+2)$-dimensions with power law nonlinearity, Chaos, 23 (2013), 15 pages
-
[54]
Q. Zhou, S. P. Moshokoa, A. Biswas, M. Belic, M. Ekici, M. Mirzazadeh, Solitons in optical metamaterials with fractional temporal evolution, Optik, 127 (2016), 10879--10897