Top

Optical and Quantum Electronics

Published in:

01-11-2017

Application of extended Fan sub-equation method to \(\mathbf {(1+1)}\)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution

Authors: Fiza Batool, Ghazala Akram

Published in: Optical and Quantum Electronics | Issue 11/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The article studies the application of the extended Fan sub-equation method to \((1+1)\)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution. This equation describes the hydromagnetic waves in cold plasma, acoustic waves in inharmonic crystals and acoustic gravity waves in compressible fluids. The structure of the extended Fan sub-equation method on the basis of time-fractional derivative is presented. The main idea of the method is to take full advantage of the general elliptic equation involving five parameters. The fractional derivatives are taken as in the sense of Jumarie’s modified Riemann–Liouville derivative. The method is reliable and gives more general exact solutions than the existing methods.

previous article Small and large signal analysis using circuit model of InGaAs/InP based uni-travel carrier photodiode

next article Dispersion managed dissipative solitons with higher order nonlinearity and frequency-selective feedback

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Akram, G., Batool, F.: Solitary wave solutions of the Schäfer-Wayne short-pulse equation using two reliable methods. Opt. Quantum Electron. 49(1), 14 (2017)CrossRef

Akram, G., Batool, F.: A class of traveling wave solutions for space-time fractional biological population model in mathematical physics. Indian. J. Phys. (2017). doi:10.1007/s12648-017-1007-1

Baskonus, H.M.: New acoustic wave behaviors to the Davey–Stewartson equation with power-law nonlinearity arising in fluid dynamics. Nonlinear Dyn. 86(1), 177–183 (2016)CrossRefMathSciNet

Baskonus, Haci Mehmet, Hasan, Bulut: Analytical studies on the \((1+1)-\)dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation defined by seismic sea waves. Waves in Random and Complex Media 25(4), 576–586 (2015)ADSCrossRefMathSciNet

Batool, F., Akram, G.: A novel approach for solitart wave solutions of the Generalized fractional Zakharov–Kuznetsov equation. Indian. J. Phys. (2017). doi:10.1007/s12648-017-1071-6

Batool, F., Akram, G.: Solitary wave solutions of (2+ 1)-dimensional soliton equation arising in mathematical physics. Optik-Int. J. Light and Electron. Opt. 144, 156–162 (2017). doi:10.1016/j.ijleo.2017.06.079 CrossRef

Batool, F., Akram, G.: On the solitary wave dynamics of complex Ginzburg-Landau equation with cubic nonlinearity. Opt. Quantum Electron. 49(4), 129 (2017)CrossRef

Benjamin, T.B., Bona, J.L., Mahony, J.J.: Model equations for long waves in nonlinear dispersive system. Philos. Trans. R. Soc. Lond. Ser. A: Math. Phys. Sci. 272, 47–78 (1972)ADSCrossRefMATHMathSciNet

Dai, C.Q., Wang, Y., Liu, J.: Spatiotemporal Hermite–Gaussian solitons of a \((3 + 1)-\)dimensional partially nonlocal nonlinear Schrodinger equation. Nonlinear Dynamics 84, 1157–1161 (2016)CrossRefMATHMathSciNet

Guner, O., Atik, H., Kayyrzhanovich, A.A.: New exact solution for space-time fractional differential equations via \((G/G)-\)expansion method. Optik-Int. J. Light and Electron. Opt. 130, 696–701 (2017)CrossRef

Gurefe, Y., Misirli, E.: Exp-function method for solving nonlinear evolution equations with higher order nonlinearity. Comput. Math. Appl. 61(8), 2025–2030 (2011)CrossRefMATHMathSciNet

Jumarie, G.: Table of some basic fractional calculus formulae derived from a modified Riemann–Liouville derivative for non differentiable functions. Appl. Math. Lett. 22(3), 378–385 (2009)CrossRefMATHMathSciNet

Li, Z.B., He, J.H.: Fractional complex transform for fractional differential equations. Math. Comput. Appl. 15(5), 970–973 (2010)MATHMathSciNet

Mirzazadeh, M., Biswas, A.: Optical solitons with spatio-temporal dispersion by first integral approach and functional variable method. Optik-Int. J. Light and Electron. Opt. 125(19), 5467–5475 (2014)CrossRef

Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoullis equation approach. Nonlinear Dyn. 81(4), 1933–1949 (2015)CrossRefMATHMathSciNet

Tariq, H., Akram, G.: New traveling wave exact and approximate solutions for the nonlinear CahnAllen equation: evolution of a nonconserved quantity. Nonlinear Dyn. 88(581), 1–14 (2016)

Tariq, H., Akram, G.: New approach for exact solutions of time fractional Cahn–Allen and time fractional Phi-4 equation. Physica A 473, 352–362 (2017)ADSCrossRefMathSciNet

Triki, H., Wazwaz, A.M.: Bright and dark soliton solutions for a K\((m, n)\) equation with t-dependent coefficients. Phys. Lett. A 373(25), 2162–2165 (2009)ADSCrossRefMATH

Wazwaz, A.M.: A sine-cosine method for handlingnonlinear wave equations. Math. Comput. Model. 40(5), 499–508 (2004)CrossRefMATH

Yomba, E.: The extended Fan sub-equation method and its application to the \((2+ 1)-\)dimensional dispersive long wave and Whitham–Broer–Kaup equations. Chin. J. Phys. 43(4), 789–805 (2005)MathSciNet

Yomba, E.: The extended Fan’s sub-equation method and its application to KdV-MKdV. BKK and Var. Boussinesq Equ. Phys. Lett. A 336(6), 463–476 (2005)CrossRefMATHMathSciNet

Yusufolu, E.: New solitonary solutions for the MBBM equations using exp-function method. Phys. Lett. A 372, 442446 (2008)

Zayed, E.M.E., Al-Joudi, S.: Applications of an extended \((\frac{G}{G})-\)expansion method to find exact solutions of nonlinear PDEs in mathematical physics. Math. Prob. Eng. 2010(2010), 19 (2010)MATHMathSciNet

Title: Application of extended Fan sub-equation method to -dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution
Authors: Fiza Batool
Ghazala Akram
Publication date: 01-11-2017
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 11/2017
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-017-1212-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 11/2017

A reconfigurable photonic microwave mixer using a dual-polarization modulator

New analytic solutions of the fractional Vakhnenko–Parkes equation

Exact solutions for Fitzhugh–Nagumo model of nerve excitation via Kudryashov method

Rabi oscillations of optical modes in a waveguide with dynamic modulation

Novel hyperbolic behaviors to some important models arising in quantum science

Preparation and characteristics study of diamond like carbon/silicon heterojunction photodetector by pulsed laser deposition