HYPERBOLIC TYPE SOLUTIONS FOR THE COUPLE BOITI-LEON-PEMPINELLI SYSTEM

Asif Yokus, Hülya Durur, Hijaz Ahmad

DOI Number
https://doi.org/10.22190/FUMI2002523Y
First page
523
Last page
531

Abstract


In this paper, the (1/G')-expansion method is used to solve the coupled Boiti-Leon-Pempinelli (CBLP) system. The proposed method was used to construct hyperbolic type solutions of the nonlinear evolution equations. To asses the applicability and effectiveness of this method, some nonlinear evolution equations have been investigated in this study. It is shown that with the help of symbolic computation, the (1/G')-expansion method provides a powerful and straightforward mathematical tool for solving nonlinear partial differential equations.


Keywords

nonlinear evolution equations; partial differential equations; symbolic computation

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References


A. Kurt, O. Tas ¸bozan and H. Durur: The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundamental

Journal of Mathematics and Applications, 2019, 2(2), pp. 173–179.

H. M. Sedighi and K. H. Shirazi: Using homotopy analysis method to determine profile for disk cam by means of optimization of dissipated energy. International Review of Mechanical Engineering, 2011, 5(5), pp. 941–946.

J. H. He: Comparison of homotopy perturbation method and homotopy analysis method. Applied Mathematics and Computation, 2004, 156(2), pp. 527–539.

H. Kheiri, N. Alipour and R. Dehghani: Homotopy analysis and Homotopy-Pade methods for the modified Burgers-Korteweg-de-Vries and the Newell Whitehead equation. Mathematical Sciences, 2011, 5(1), pp. 33–50.

H. M. Sedighi and F. Daneshmand: Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term. Journal of Applied and Com-

putational Mechanics, 2014, 1(1), pp. 1–9.

J. H. He: Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and computation, 2003, 135(1), pp. 73–79.

A. Yokus ¸ and D. Kaya: Traveling wave solutions of some nonlinear partial differential equations by using extended-expansion method. Advances in Mathematical Physics, 2015.

H. Durur: Different types analytic solutions of the (1+ 1)-dimensional resonant nonlinear Schr¨ odinger’s equation using (G ′ /G)-expansion method. Modern Physics Letters

B, 2020, 34(03).

H. Ahmad, T. A. Khan and C. Cesarano: Numerical Solutions of Coupled Burgers’ Equations. Axioms, 2019, 8(4).

H. Ahmad, T. A. Khan and S. Yao: Numerical solution of second order Painlev´ e differential equation. Journal of Mathematics and Computer Science, 2020, 21(2), pp.

–157.

H. Ahmad, A.R. Seadawy, T.A. Khan and P. Thounthong: Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations. Journal of Taibah University for Science, 2020, 14(1), pp. 346–358.

H. Durur, O. Tas ¸bozan, A. Kurt and M. S ¸enol: New Wave Solutions of Time Fractional Kadomtsev-Petviashvili Equation Arising In the Evolution of Nonlinear Long Waves of Small Amplitude. Erzincan University Journal of the Institute of Science and Technology, 2019, 12(2), pp. 807–815.

H. Ahmad: Variational iteration method with an auxiliary parameter for solving differential equations of the fifth order. Nonlinear Science Letters A. 2018, 9(1), pp. 27–35.

M. Rafiq, H. Ahmad, S.T. Mohyud-Din: Variational iteration method with an auxiliary parameter for solving Volterra’s population model. Nonlinear Science Letters

A. 2017, 8(4), pp. 389–396.

H. Ahmad, M. Rafiq, C. Cesarano and H. Durur: Variational iteration algorithm-I with an auxiliary parameter for solving boundary value problems. Earthline

Journal of Mathematical Sciences, 2020, 3(2), pp. 229–247.

H. Ahmad and T. A. Khan: Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations. Journal of Low Frequency Noise, Vibration and Active Control, 2019, 38(3-4), pp. 1113–1124.

M. Yavuz and N. Ozdemır: An Integral Transform Solution for Fractional Advection-Diffusion Problem. Mathematical Studies and Applications, 2018, 4-6 October, 442.

A. Yokus ¸ and H. Durur: Complex hyperbolic traveling wave solutions of Kuramoto-Sivashinsky equation using (1/G ′ ) expansion method for nonlinear dynamic theory.

Journal of Balıkesir University Institute of Science and Technology, 2019, 21(2), pp. 590–599.

H. Durur and A. Yokus ¸: (1/G ′ )-A¸ cılım Metodunu Kullanarak Sawada–Kotera Den-kleminin Hiperbolik Yürüyen Dalga C¸özümleri. Afyon Kocatepe Universitesi Fen ve Mühendislik Bilimleri Dergisi, 2019, 19(3), pp. 615–619.

J. H. He: Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computation, 2000, 114(2-3), pp. 115–123.

J. H. He: Variational iteration method—some recent results and new interpretations. Journal of computational and applied mathematics, 2007, 207(1), pp. 3–17.

D. Kaya, A. Yokus ¸ and U. Demiro˘ glu: Comparison of Exact and Numerical Solutions for the Sharma–Tasso–Olver Equation. In Numerical Solutions of Realistic Non-

linear Phenomena, 2020, pp. 53–65. Springer, Cham.

Q. Su-Ping and T. Li-Xin: Modification of the Clarkson–Kruskal Direct Method for a Coupled System. Chinese Physics Letters, 2007, 24(10), 2720.

F. Dusunceli: New Exact Solutions for Generalized (3+ 1) Shallow Water-Like (SWL) Equation. Applied Mathematics and Nonlinear Sciences, 2019, 4(2), pp. 365–

D. Kaya and A. Yokus ¸: A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations. Mathematics and

Computers in Simulation, 2002, 60(6), pp. 507–512.

D. Kaya and A. Yokus ¸: A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations. Applied Mathematics

and Computation, 2005, 164(3), pp. 857–864.

A. Yokus and D. Kaya: A numerical comparison for coupled boussinesq equations by using the ADM. In: Proceedings, 2004, pp. 730–736.

M. Yavuz and N. Ozdemır: A quantitative approach to fractional option pricing problems with decomposition series. Konuralp Journal of Mathematics, 2018, 6(1), pp.

–109.

H. Ahmad, T.A. Khan, P. S. Stanimirovic and I. Ahmad: Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV Type Equations. Journal of Applied and Computational Mechanics, 2020.

H. Ahmad, A. R. Seadawy, T. A. Khan: Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration

algorithm. Mathematics and Computers in Simulation, 2020.

H. Ahmad, A. R. Seadawy, T. A. Khan: Numerical solution of Korteweg–de VriesBurgers equation by the modified variational iteration algorithm-II arising in shallow

water waves. Physica Scripta, 2020, 95(4).

M. Darvishi, S. Arbabi, M. Najafi and A. Wazwaz: Traveling wave solutions of a (2+ 1)-dimensional Zakharov-like equation by the first integral method and the tanh

method. Optik, 2016, 127(16), pp. 6312–6321.

A. A. Rady, E. S. Osman and M. Khalfallah: The homogeneous balance method and its application to the Benjamin–Bona–Mahoney (BBM) equation. Applied Math-

ematics and Computation, 2010, 217(4), pp. 1385–1390.

D. Kumar, A. R. Seadawy and A. K. Joardar: Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in

mathematical biology. Chinese journal of physics, 2018, 56(1), pp. 75–85.

H. Durur, M. S ¸enol, A. Kurt and O. Tas ¸bozan: Zaman-Kesirli Kadomtsev-Petviashvili Denkleminin Conformable Türev ile Yakla¸ sık C¸özümleri. Erzincan University Journal of the Institute of Science and Technology, 2019, 12(2), pp. 796–806.

I. Aziz and B. ˇ Sarler: The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets. Mathematical and Computer Modelling, 2010, 52(9-10), pp. 1577–1590.

T. A. Sulaiman and H. Bulut: The new extended rational SGEEM for construction of optical solitons to the (2+1)-dimensional Kundu–Mukherjee–Naskar model. Applied Mathematics and Nonlinear Sciences, 2019, 4(2), pp. 513–522.

H. M. Baskonus, H. Bulut and T. A. Sulaiman: New complex hyperbolic struc-

tures to the lonngren-wave equation by using sine-gordon expansion method. Applied Mathematics and Nonlinear Sciences, 2019, 4(1), pp. 129–138.

E. ˙ I. Eskitas ¸c ¸ıo˘ glu, M. B. Aktas ¸ and H. M. Baskonus: New complex and hyperbolic forms for Ablowitz–Kaup–Newell–Segur wave equation with fourth order. Applied Mathematics and Nonlinear Sciences, 2019, 4(1), pp. 105–112.

A. Yokus and S. Gülbahar: Numerical solutions with linearization techniques of the fractional harry dym equation. Applied Mathematics and Nonlinear Sciences, 2019, 4(1), pp. 35–42.

H. Ahmad: Variational iteration algorithm-II with an auxiliary parameter and its optimal determination. Nonlinear Science Letters A, 2018, 9(1), pp. 62–72.

H. M. Sedighi, K. H. Shirazi and M. A. Attarzadeh: A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches. Acta Astronautica,

, 19, pp. 245–250.

H. Ahmad, T. A. Khan: Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass-spring

systems. Noise & Vibration Worldwide, 2020, 51(1-2), pp. 12–20.

M. F. Aghdaei and J. M. Heris: Exact Solutions of the Couple Boiti-Leon-Pempinelli System by the Generalized (G ′ /G)-expansion Method. Journal of Mathematical Extension, 2011, 5(2), pp. 91–104.

M. A. Abdelrahman and M. M. Khater: Traveling wave solutions for the couple Boiti-Leon-Pempinelli system by using extended Jacobian elliptic function expansion

method. Journal of Advances in Physics, 2019, 11(3).




DOI: https://doi.org/10.22190/FUMI2002523Y

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