The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Manafian, Jalil; Ilhan, Onur Alp; Avazpour, Laleh

doi:10.1515/ijnsns-2019-0279

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Journal Article · 16 September 2020 · International Journal of Nonlinear Sciences and Numerical Simulation

DOI:https://doi.org/10.1515/ijnsns-2019-0279· OSTI ID:1851140

^[1]; Ilhan, Onur Alp ^[2]; Avazpour, Laleh ^[3]

Department of Applied Mathematics , Faculty of Mathematical Sciences, University of Tabriz , Tabriz , Iran; OSTI
Department of Mathematics , Faculty of Education, Erciyes University , 38039, Melikgazi-Kayseri , Turkey
Department of Electrical and Computer Engineering , University of Wisconsin-Madison , Madison , WI , 53706, USA

Abstract

In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense ofβ-derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation ofβ-derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Research Organization:: Univ. of Wisconsin, Madison, WI (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0008712;

OSTI ID:: 1851140

Journal Information:: International Journal of Nonlinear Sciences and Numerical Simulation, Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation Journal Issue: 1 Vol. 22; ISSN 1565-1339

Country of Publication:: United States

Language:: English

References (52)

Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses Dehghan, Mehdi; Heris, Jalil Manafian; Saadatmandi, Abbas Mathematical Methods in the Applied Sciences https://doi.org/10.1002/mma.1329	journal	January 2010
Wave solutions for variants of the KdV-Burger and the K ( n , n )-Burger equations by the generalized G′/G-expansion method: J. MANAFIAN AND C. TEYMURI SINDI Teymuri Sindi, Cevat; Manafian, Jalil Mathematical Methods in the Applied Sciences, Vol. 40, Issue 12 https://doi.org/10.1002/mma.4309	journal	January 2017
The new complex rational function prototype structures for the nonlinear Schrödinger-inviscid burgers system Saha Ray, Santanu Mathematical Methods in the Applied Sciences, Vol. 41, Issue 16 https://doi.org/10.1002/mma.5140	journal	July 2018
Solving nonlinear fractional partial differential equations using the homotopy analysis method: Nonlinear Fractional Partial Differential Equations Dehghan, Mehdi; Manafian, Jalil; Saadatmandi, Abbas Numerical Methods for Partial Differential Equations, Vol. 26, Issue 2 https://doi.org/10.1002/num.20460	journal	July 2009
Chebyshev polynomials for the numerical solution of fractal–fractional model of nonlinear Ginzburg–Landau equation Heydari, M. H.; Atangana, A.; Avazzadeh, Z. Engineering with Computers, Vol. 37, Issue 2 https://doi.org/10.1007/s00366-019-00889-9	journal	November 2019
An efficient wavelet-based approximation method for the coupled nonlinear fractal–fractional 2D Schrödinger equations Heydari, M. H.; Hosseininia, M.; Avazzadeh, Z. Engineering with Computers, Vol. 37, Issue 3 https://doi.org/10.1007/s00366-020-00934-y	journal	January 2020
Dispersive dark optical soliton with Tzitzéica type nonlinear evolution equations arising in nonlinear optics: Dispersive dark optical soliton with Tzitzéica ... Manafian, Jalil; Lakestani, Mehrdad Optical and Quantum Electronics, Vol. 48, Issue 2 https://doi.org/10.1007/s11082-016-0371-y	journal	January 2016
Exact solutions for nonlinear fractional differential equations using exponential rational function method Mohyud-Din, Syed Tauseef; Bibi, Sadaf Optical and Quantum Electronics, Vol. 49, Issue 2 https://doi.org/10.1007/s11082-017-0895-9	journal	January 2017
Optical solitons in $$(n+1)$$ ( n + 1 ) -dimensions under anti-cubic law of nonlinearity by analytical methods Foroutan, Mohammadreza; Manafian, Jalil; Ranjbaran, Arash Optical and Quantum Electronics, Vol. 50, Issue 2 https://doi.org/10.1007/s11082-018-1366-7	journal	February 2018
Solitary wave and periodic wave solutions for Burgers, Fisher, Huxley and combined forms of these equations by the (G ′ /G)-expansion method Manafian, Jalil; Lakestani, Mehrdad Pramana, Vol. 85, Issue 1 https://doi.org/10.1007/s12043-014-0887-2	journal	February 2015
Lump-type solutions and interaction phenomenon to the bidirectional Sawada–Kotera equation Manafian, Jalil; Lakestani, Mehrdad Pramana, Vol. 92, Issue 3 https://doi.org/10.1007/s12043-018-1700-4	journal	February 2019
Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions Heydari, M. H.; Hooshmandasl, M. R.; Mohammadi, F. Applied Mathematics and Computation, Vol. 234 https://doi.org/10.1016/j.amc.2014.02.047	journal	May 2014
Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation Manafian, Jalil; Mohammadi-Ivatloo, Behnam; Abapour, Mehdi Applied Mathematics and Computation, Vol. 356 https://doi.org/10.1016/j.amc.2019.03.016	journal	September 2019
An efficient computational method for solving fractional biharmonic equation Heydari, M. H.; Hooshmandasl, M. R.; Maalek Ghaini, F. M. Computers & Mathematics with Applications, Vol. 68, Issue 3 https://doi.org/10.1016/j.camwa.2014.06.001	journal	August 2014
Novel solitary wave solutions for the ( 3 + 1 ) -dimensional extended Jimbo–Miwa equations Manafian, Jalil Computers & Mathematics with Applications, Vol. 76, Issue 5 https://doi.org/10.1016/j.camwa.2018.06.018	journal	September 2018
Lump wave solutions and the interaction phenomenon for a variable-coefficient Kadomtsev–Petviashvili equation Ilhan, Onur Alp; Manafian, Jalil; Shahriari, Mohammad Computers & Mathematics with Applications, Vol. 78, Issue 8 https://doi.org/10.1016/j.camwa.2019.03.048	journal	October 2019
New double periodic exact solutions of the coupled Schrödinger–Boussinesq equations describing physical processes in laser and plasma physics Ray, S. Saha Chinese Journal of Physics, Vol. 55, Issue 5 https://doi.org/10.1016/j.cjph.2017.08.022	journal	October 2017
Application of tan(ϕ/2)-expansion method for solving the Biswas–Milovic equation for Kerr law nonlinearity Manafian, Jalil; Lakestani, Mehrdad Optik, Vol. 127, Issue 4 https://doi.org/10.1016/j.ijleo.2015.11.078	journal	February 2016
Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan(Φ(ξ)/2)-expansion method Manafian, Jalil Optik, Vol. 127, Issue 10 https://doi.org/10.1016/j.ijleo.2016.01.078	journal	May 2016
Optical soliton solutions for the Gerdjikov–Ivanov model via tan(ϕ/2)-expansion method Manafian, Jalil; Lakestani, Mehrdad Optik, Vol. 127, Issue 20 https://doi.org/10.1016/j.ijleo.2016.07.032	journal	October 2016
The analytical study of solitons to the nonlinear Schrödinger equation with resonant nonlinearity Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah Optik, Vol. 130 https://doi.org/10.1016/j.ijleo.2016.10.098	journal	February 2017
Application of the generalized G′/G-expansion method for nonlinear PDEs to obtaining soliton wave solution Manafian, Jalil; Aghdaei, Mehdi Fazli; Khalilian, Morteza Optik, Vol. 135 https://doi.org/10.1016/j.ijleo.2017.01.078	journal	April 2017
New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method Kumar, Dipankar; Manafian, Jalil; Hawlader, Faisal Optik, Vol. 160 https://doi.org/10.1016/j.ijleo.2018.01.137	journal	May 2018
Numerical simulations for fractional variation of (1 + 1)-dimensional Biswas-Milovic equation Korpinar, Zeliha; Inc, Mustafa Optik, Vol. 166 https://doi.org/10.1016/j.ijleo.2018.02.099	journal	August 2018
Optical solitons and stability analysis with spatio-temporal dispersion in Kerr and quadric-cubic nonlinear media Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi Optik, Vol. 178 https://doi.org/10.1016/j.ijleo.2018.10.046	journal	February 2019
Optical soliton solutions of the NLSE with quadratic-cubic-Hamiltonian perturbations and modulation instability analysis Aslan, Ebru Cavlak Optik, Vol. 196 https://doi.org/10.1016/j.ijleo.2019.04.008	journal	November 2019
New optical solitons for Biswas–Arshed equation with higher order dispersions and full nonlinearity Korpinar, Zeliha; Inc, Mustafa; Bayram, Mustafa Optik, Vol. 206 https://doi.org/10.1016/j.ijleo.2019.163332	journal	March 2020
Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability Seadawy, Aly R.; Lu, Dianchen; Yue, Chen Journal of Taibah University for Science, Vol. 11, Issue 4 https://doi.org/10.1016/j.jtusci.2016.06.002	journal	July 2017
Dispersive optical solitons of time-fractional Schrödinger–Hirota equation in nonlinear optical fibers Saha Ray, S. Physica A: Statistical Mechanics and its Applications, Vol. 537 https://doi.org/10.1016/j.physa.2019.122619	journal	January 2020
Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation Xu, Fei Physics Letters A, Vol. 372, Issue 3 https://doi.org/10.1016/j.physleta.2007.07.035	journal	January 2008
Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma Seadawy, A. R.; El-Rashidy, K. Results in Physics, Vol. 8 https://doi.org/10.1016/j.rinp.2018.01.053	journal	March 2018
New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod Seadawy, Aly R.; Manafian, Jalil Results in Physics, Vol. 8 https://doi.org/10.1016/j.rinp.2018.01.062	journal	March 2018
Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik-Novikov-Vesselov dynamical equation Iqbal, Mujahid; Seadawy, Aly R.; Khalil, Omar H. Results in Physics, Vol. 16 https://doi.org/10.1016/j.rinp.2019.102838	journal	March 2020
Chirped solitons in negative index materials generated by Kerr nonlinearity Houwe, A.; Inc, Mustafa; Doka, S. Y. Results in Physics, Vol. 17 https://doi.org/10.1016/j.rinp.2020.103097	journal	June 2020
Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity Seadawy, Aly R.; Iqbal, Mujahid; Lu, Dianchen Journal of Taibah University for Science, Vol. 13, Issue 1 https://doi.org/10.1080/16583655.2019.1680170	journal	October 2019
Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations Ahmad, Hijaz; Seadawy, Aly R.; Khan, Tufail A. Journal of Taibah University for Science, Vol. 14, Issue 1 https://doi.org/10.1080/16583655.2020.1741943	journal	January 2020
A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws Özkan, Yeşim Sağlam; Yaşar, Emrullah; Seadawy, Aly R. Journal of Taibah University for Science, Vol. 14, Issue 1 https://doi.org/10.1080/16583655.2020.1760513	journal	January 2020
Optical solitons in medium with parabolic law nonlinearity and higher order dispersion Zhou, Qin; Zhu, Qiuping Waves in Random and Complex Media, Vol. 25, Issue 1 https://doi.org/10.1080/17455030.2014.956847	journal	September 2014
Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics Baskonus, Haci Mehmet; Bulut, Hasan Waves in Random and Complex Media, Vol. 26, Issue 2 https://doi.org/10.1080/17455030.2015.1132860	journal	December 2015
Optical solitons in a power-law media with fourth-order dispersion by three integration methods Manafian, Jalil Cogent Mathematics & Statistics, Vol. 5, Issue 1 https://doi.org/10.1080/23311835.2018.1434924	journal	January 2018
Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics Dehghan, Mehdi; Manafian Heris, Jalil; Saadatmandi, Abbas International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21, Issue 6 https://doi.org/10.1108/09615531111148482	journal	August 2011
Optical solitons with Biswas-Milovic equation for Kerr law nonlinearity Manafian, Jalil; Lakestani, Mehrdad The European Physical Journal Plus, Vol. 130, Issue 4 https://doi.org/10.1140/epjp/i2015-15061-1	journal	April 2015
On the complex structures of the Biswas-Milovic equation for power, parabolic and dual parabolic law nonlinearities Manafian, Jalil The European Physical Journal Plus, Vol. 130, Issue 12 https://doi.org/10.1140/epjp/i2015-15255-5	journal	December 2015
The nonlinear dispersive Davey-Stewartson system for surface waves propagation in shallow water and its stability Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua The European Physical Journal Plus, Vol. 131, Issue 12 https://doi.org/10.1140/epjp/i2016-16425-7	journal	December 2016
Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas Sindi, Cevat Teymuri; Manafian, Jalil The European Physical Journal Plus, Vol. 132, Issue 2 https://doi.org/10.1140/epjp/i2017-11354-7	journal	February 2017
Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods Iqbal, Mujahid; seadawy, Aly R.; Lu, Dianchen Modern Physics Letters A, Vol. 33, Issue 32 https://doi.org/10.1142/S0217732318501833	journal	October 2018
ANALYTICAL TREATMENT OF SOME PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MATHEMATICAL PHYSICS BY USING THE Exp -FUNCTION METHOD Dehghan, Mehdi; Manafian, Jalil; Saadatmandi, Abbas International Journal of Modern Physics B, Vol. 25, Issue 22 https://doi.org/10.1142/S021797921110148X	journal	September 2011
New soliton solutions of conformable time fractional Caudrey–Dodd–Gibbon–Sawada–Kotera equation in modeling wave phenomena Saha Ray, S. Modern Physics Letters B, Vol. 33, Issue 18 https://doi.org/10.1142/S0217984919502026	journal	June 2019
The new soliton wave solutions of conformable time-fractional Rosenau–Kawahara-RLW equation Sahoo, S.; Ray, S. Saha Modern Physics Letters B, Vol. 33, Issue 29 https://doi.org/10.1142/S0217984919503652	journal	October 2019
New Improvement of the Expansion Methods for Solving the Generalized Fitzhugh-Nagumo Equation with Time-Dependent Coefficients Manafian, Jalil; Lakestani, Mehrdad International Journal of Engineering Mathematics, Vol. 2015 https://doi.org/10.1155/2015/107978	journal	December 2015
The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method Dehghan, Mehdi; Manafian, Jalil Zeitschrift für Naturforschung A, Vol. 64, Issue 7-8 https://doi.org/10.1515/zna-2009-7-803	journal	August 2009
New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model Atangana, Abdon; Baleanu, Dumitru Thermal Science, Vol. 20, Issue 2 https://doi.org/10.2298/TSCI160111018A	journal	January 2016

Similar Records

Boundary value methods for PDEs

Conference · 1994 · OSTI ID:482022

Solitary wave dynamics in time-dependent potentials

Journal Article · 2008 · Journal of Mathematical Physics · OSTI ID:21100225

Use of Particular Analytical Solutions for Calculations of Nonlinear PDEs

Journal Article · 2008 · AIP Conference Proceedings · OSTI ID:21251622

Related Subjects

Engineering
Mathematics
Mechanics
Physics

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Citation Formats

References (52)

Similar Records

Related Subjects