ELLIPTIC FUNCTION SOLUTIONS FOR SOME NONLINEAR PDES IN MATHEMATICAL PHYSICS

Yusuf Gurefe; Yusuf Pandir; Tolga Akturk; Hasan Bulut

doi:10.11948/2017024

2017 Volume 7 Issue 1

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Yusuf Gurefe, Yusuf Pandir, Tolga Akturk, Hasan Bulut. ELLIPTIC FUNCTION SOLUTIONS FOR SOME NONLINEAR PDES IN MATHEMATICAL PHYSICS[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 372-391. doi: 10.11948/2017024

Citation:

Yusuf Gurefe, Yusuf Pandir, Tolga Akturk, Hasan Bulut. ELLIPTIC FUNCTION SOLUTIONS FOR SOME NONLINEAR PDES IN MATHEMATICAL PHYSICS[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 372-391. doi: 10.11948/2017024

ELLIPTIC FUNCTION SOLUTIONS FOR SOME NONLINEAR PDES IN MATHEMATICAL PHYSICS

1 Department of Econometrics, Faculty of Economics and Administrative Sciences, Usak University, 64200 Usak, Turkey;
2 Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey;
3 Department of Mathematics, Faculty of Science, Firat University, 23100 Elazig, Turkey

Abstract

Abstract

In this work, we have constructed various types of soliton solutions of the generalized regularized long wave and generalized nonlinear KleinGordon equations by the using of the extended trial equation method. Some of the obtained exact traveling wave solutions to these nonlinear problems are the rational function, 1-soliton, singular, the elliptic integral functions F,E,Π and the Jacobi elliptic function sn solutions. Also, all of the solutions are compared with the exact solutions in literature, and it is seen that some of the solutions computed in this paper are new wave solutions.
- Extended trial equation method /
- generalized regularized long wave /
- generalized Klein-Gordon equation /
- soliton solutions /
- elliptic solutions
MSC: 35C07;35C08;37K40

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References

[1]	M. A. Abdou and E. M. Abulwafa, Application of the Exp-Function method to the Riccati equation and new exact solutions with three arbitrary functions of quantum Zakharov equations, Z. Naturforsch., 63a(2008), 646-652. Google Scholar
[2]	A. H. A. Ali, A. A. Soliman, and K. R. Raslan, Soliton solution for nonlinear partial differential equations by cosine-function method, Phys. Lett., A 368(2007), 299-304. Google Scholar
[3]	M. T. Alquran, Solitons and periodic solutions to nonlinear partial differential equations by the sine-cosine method, Appl. Math. Inf. Sci., 6(2012), 85-88. Google Scholar
[4]	H. Bulut, Y. Pandir and S.T. Demiray, Exact solutions of nonlinear Schrodinger's equation with dual power-law nonlinearity by extended trial equation method, Waves in Random and Complex Media, 24(2014)(4), 439-451. Google Scholar
[5]	Z. D. Dai, C. J. Wang, S. Q. Lin, D. L. Li, and G. Mu, The three-wave method for nonlinear evolution equations, Nonl. Sci. Lett., A1(2010)(1), 77-82. Google Scholar
[6]	X. H. Du, An irrational trial equation method and its applications, Pramana-J. Phys., 75(2010), 415-422. Google Scholar
[7]	A. Ebaid, Exact solutions for the generalized Klein-Gordon equation via a transformation and Exp-function method and comparison with Adomian's method, J. Comput. Appl. Math., 223(2009), 278-290. Google Scholar
[8]	G. Ebadi, E. V. Krishnan, and A. Biswas, Solitons and cnoidal waves of the Klein-Gordon-Zakharov equation in plasmas, Pramana-J. Phys., 79(2012), 185-198. Google Scholar
[9]	M. K. Elboree, Hyperbolic and trigonometric solutions for some nonlinear evolution equations, Commun. Nonl. Sci. Numer. Simulat., 17(2012), 4085-4096. Google Scholar
[10]	Y. Gurefe and E. Misirli, New variable separation solutions of two-dimensional Burgers system, Appl. Math. Comput., 217(2011), 9189-9197. Google Scholar
[11]	Y. Gurefe, E. Misirli, A. Sonmezoglu, and M. Ekici, Extended trial equation method to generalized nonlinear partial differential equations, Appl. Math. Comput., 219(2013), 5253-5260. Google Scholar
[12]	Y. Gurefe, A. Sonmezoglu, and E. Misirli, Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics, Pramana-J. Phys., 7(2011), 1023-1029. Google Scholar
[13]	J. H. He, Asymptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012(2012), 130 pages. Google Scholar
[14]	H. Jia and W. Xu, Solitons solutions for some nonlinear evolution equations, Appl. Math. Comput., 217(2010), 1678-1687. Google Scholar
[15]	N. A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonl. Sci. Numer. Simulat., 17(2012), 2248-2253. Google Scholar
[16]	C. S. Liu, Trial equation method and its applications to nonlinear evolution equations, Acta. Phys. Sin., 54(2005), 2505-2509. Google Scholar
[17]	C. S. Liu, A new trial equation method and its applications, Commun. Theor. Phys., 45(2006), 395-397. Google Scholar
[18]	C. S. Liu, Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations, Comput. Phys. Commun., 181(2010), 317-324. Google Scholar
[19]	J. Liu, G. Mua, Z. Dai, and X. Liu, Analytic multi-soliton solutions of the generalized Burgers equation, Comput. Math. Appl., 61(2011), 1995-1999. Google Scholar
[20]	W. X. Ma, T. Huang, and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application, Phys. Scr., 82(2010), 065003, 8 pages. Google Scholar
[21]	J. Nickel and H. W. Schurmann, 2-soliton-solution of the Novikov-Veselov equation, Int. J. Theor. Phys., 45(2006), 1825-1829. Google Scholar
[22]	Y. Pandir, Y. Gurefe, U. Kadak, and E. Misirli, Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstr. Appl. Anal., 2012(2012), 16 pages. Google Scholar
[23]	Y. Pandir, Y. Gurefe, and E. Misirli, Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation, Phys. Scripta, 87(2013), 025003 p12. Google Scholar
[24]	Y. Pandir, New exact solutions of the generalized Zakharov-Kuznetsov modified equal-width equation, Pramana-J. Phys., 82(2014)(6), 949-964. Google Scholar
[25]	Y. Pandir, Y. Gurefe, and E. Misirli, A new approach to Kudryashov's method for solving some nonlinear physical models, Int. J. Phys. Sci., 7(2012), 2860-2866. Google Scholar
[26]	P. N. Ryabov, D. I. Sinelshchikov, and M. B. Kochanov, Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations, Appl. Math. Comput., 218(2011), 3965-3972. Google Scholar
[27]	Y. Shi, Z. Dai, and D. Li, Application of Exp-function method for 2D cubicquintic Ginzburg-Landau equation, Appl. Math. Comput., 210(2009), 269-275. Google Scholar
[28]	A. M. Wazwaz, Special types of the nonlinear dispersive Zakharov-Kuznetsov equation with compactons, solitons and periodic solutions, Int. J. Comput. Math., 81(2004)(81), 1107-1119. Google Scholar
[29]	Y. Xie and J. Tang, The superposition method in seeking the solitary wave solutions to the KdV-Burgers equation, Pramana-J. Phys., 66(2006), 479-483. Google Scholar
[30]	J. R. Yang and J. J. Mao, Soliton solutions of coupled KdV system from Hirota's bilinear direct method, Commun. Theor. Phys., 49(2008), 22-26. Google Scholar
[31]	E. Zayed, M. Abdelaziz, and M. Elmalky, Enhanced (G'/G)-expansion method and applications to the (2+1)D typical breaking soliton and Burgers equations, J. Adv. Math. Stud., 4(2011), 109-122. Google Scholar