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References
|
Abdou MA (2007). The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos Solitons Fractals 31:95–104. Crossref |
||||
|
Alam MN, Akbar MA (2013). Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized -expansion method. Springer Plus. 2:617. DOI: 10.1186/2193-1801-2-617. Crossref |
||||
|
Alam MN, Akbar MA (2014a). Traveling wave solutions for the mKdV equation and the Gardner equation by new approach of the generalized -expansion method. J. Egyptian Math. Soc. 22:402-406. Crossref |
||||
| Alam MN, Akbar MA (2014b). Application of the new approach of generalized -expansion method to find exact solutions of nonlinear PDEs in mathematical physics. BIBECHANA. 10:58-70. | ||||
| Alam MN, Akbar MA, Fetama K, Hatez MG (2014a). Exact traveling wave solutions of the (2+1)-dimensional modified Zakharov-Kuznetsov equation via new extended -expansion method. Elixir Appl. Math. 73:26267-26276. | ||||
|
Alam MN, Akbar MA, Hoque MF (2014b). Exact traveling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation using new approach of the generalized -expansion method. Pramana J. Phys. 83:317-329. Crossref |
||||
|
Alam MN, Akbar MA, Mohyud-Din ST (2014c). A novel -expansion method and its application to the Boussinesq equation. Chin. Phys. B. 23:020203-020210. Crossref |
||||
|
Alam MN, Akbar MA, Mohyud-Din ST (2014d). General traveling wave solutions of the strain wave equation in microstructured solids via the new approach of generalized -Expansion method. Alexandria Eng. J. 53:233–241. Crossref |
||||
| Alam MN, Akbar MA (2015). Some new exact traveling wave solutions to the simplified MCH equation and the (1+1)-dimensional combined KdV-mKdV equations. J. Assoc. Arab Univ. Basic Appl. Sci. 17:6–13. | ||||
|
Alquran M, Al-Khaled K (2011a). The tanh and sine-cosine methods for higher order equations of Korteweg-de Vries type. Physica Scripta. 84:025010. Crossref |
||||
|
Alquran M, Al-Khaled K (2011b). Sinc and solitary wave solutions to the generalized Benjamin-Bona-Mahony- Burgers equations. Physica Scripta. 83: 065010. Crossref |
||||
| Alquran M (2012). Solitons and periodic solutions to nonlinear partial differential equations by the Sine- Cosine method. Appl. Math. Inf. Sci. 6:85-88. | ||||
|
Alquran M, Al-khaled K (2012). Mathematical methods for a reliable treatment of the (2+1)-dimensional Zoomeron equation. Math. Sci. 6:12 doi:10.1186/2251-7456-6-11. Crossref |
||||
| Alquran M, Ali M, Al-Khaled K (2012). Solitary wave solutions to shallow water waves arising in fluid dynamics. Nonlinear Studies. 19:555-562. | ||||
| Alquran M, Qawasmeh A (2014). Soliton solutions of shallow water wave equations by means of -expansion method. J. Appl. Anal. Comput. 3:221-229. | ||||
| Aminikhad H, Moosaei H, Hajipour M (2009). Exact solutions for nonlinear partial differential equations via Exp-function method. Numer. Methods Partial Differ. Equ. 261427–1433. | ||||
|
Bekir A, Unsal O (2012). Analytic treatment of nonlinear evolution equations using the first integral method. Pramana J. Phys. 79:3-17. Crossref |
||||
|
Bountis TC, Papageorgiou V, Winternitz P (1986). On the integrability of systems of nonlinear ordinary differential equations with superposition principles. J. Math. Phys. 27:1215-1224. Crossref |
||||
|
Conte R, Musette M (1992). Link between solitary waves and projective Riccati equations. Phys. A: Math. Cen. 25:2609-2623. Crossref |
||||
|
Dai CQ, Zhang JF (2006). Jacobian elliptic function method for nonlinear differential- difference equations. Chaos Solitons Fractals. 27:1042–1049. Crossref |
||||
|
EL-Wakil SA, Abdou MA (2007). New exact traveling wave solutions using modified extended tanh-function method. Chaos Solitons Fractals 31:840–852. Crossref |
||||
|
Fan E, Zhang H (1998). A note on the homogeneous balance method. Phys. Lett. A. 246:403–406. Crossref |
||||
|
Fan E (2000). Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A. 277:212–218. Crossref |
||||
|
Fan E, Zhang J (2002). Applications of the Jacobi elliptic function method to special type nonlinear equations, Phys. Lett. A. 305:383–392. Crossref |
||||
|
Feng ZS (2002). The first integral method to study the Burgers–KdV equation. J. Phys. A: Math. Gen. 35:343–349. Crossref |
||||
|
Hafez MG, Alam MN, Akbar MA (2014). Traveling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system. J. King Saud Univ. Sci. Crossref |
||||
|
Hayek M (2010). Constructing of exact solutions to the KdV and Burgers equations with power law nonlinearity by the extended -expansion method. Appl. Math. Comput. 217:212–221. Crossref |
||||
|
He JH, Wu XH (2006). Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30:700–708. Crossref |
||||
|
Jawad AJM, Petkovic MD, Biswas A (2010). Modified simple equation method for nonlinear evolution equations. Appl. Math. Comput. 217:869–877. Crossref |
||||
|
Liu S, Fu Z, Liu S, Zhao Q (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A. 289:69–74. Crossref |
||||
|
Lu BHQ, Zhang HQ, Xie FD (2010). Traveling wave solutions of nonlinear partial differential equations by using the first integral method. Appl. Math. Comput. 216:1329-1336. Crossref |
||||
|
Ma WX, Wu HY, He JS (2007). Partial differential equations possessing Frobenius integrable decomposition technique. Phys. Lett. A. 364:29-32. Crossref |
||||
|
Ma WX, Lee JH (2009). A transformed rational function method and exact solutions to the (3+1) dimensional Jimbo-Miwa equation. Chaos, Solitons Fractals 42:1356-1363. Crossref |
||||
|
Ma WX, Huang T, Zhang Y (2010). A multiple exp-function method for nonlinear differential equations and its application. Phys. Script. 82:065003. Crossref |
||||
|
Ma WX, Zhu Z (2012). Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm. Appl. Math. Comput. 218:11871-11879. Crossref |
||||
|
Malfiieiet W (1992). Solitary wave solutions of nonlinear wave equation. Am. J. Phys. 60:650–654. Crossref |
||||
|
Malfiieiet W, Hereman W (1996). The tanh method: Exact solutions of nonlinear evolution and wave equations. Phys. Scr. 54:563–568. Crossref |
||||
| Moosaei H, Mirzazadeh M Yildirim A (2011). Exact solutions to the perturbed nonlinear Schrodinger equation with Kerr law nonlinearity by using the first integral method. Nonlinear Anal.: Model. Control. 16:332–339. | ||||
|
Ren YJ, Zhang HQ (2006). A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation. Chaos Solitons Fractals. 27:959–979. Crossref |
||||
|
Shukri S, Al-khaled K (2010). The extended tanh method for solving systems of nonlinear wave equations. Appl. Math. Comput. 217:1997-2006. Crossref |
||||
|
Wang ML (1996). Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A. 213:279–287. Crossref |
||||
|
Wazwaz AM (2004a). The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154:714–723. Crossref |
||||
|
Wazwaz AM (2004b). A sine-cosine method for handling nonlinear wave equations. Math. Comput. Model. 40:499–508. Crossref |
||||
|
Wazwaz AM (2005). Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE Method. Comput. Math. Appl. 50:1685–1696. Crossref |
||||
|
Wazwaz AM (2007). The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Appl. Math. Comput. 187:1131–1142. Crossref |
||||
|
Yan C (1996). A simple transformation for nonlinear waves. Phys. Lett. A. 224:77-84. Crossref |
||||
|
Yang AM, Yang X J, Li ZB (2013). Local fractional series expansion method for solving wave and diffusion equations on cantor sets. Abst. Appl. Anal. Article ID 351057: P.5. Crossref |
||||
|
Yang YJ, Baleanu D, Yang XJ (2013). A Local fractional variational iteration method for Laplace equation within local fractional operators. Abst. Appl. Anal. Article ID 202650:P.6. Crossref |
||||
|
Yan ZY (2003). Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres. Chaos, Solitons Fractals 16:759-766. Crossref |
||||
| Yomba E (2005). The general projective Riccati equations method and exact solutions for a class of nonlinear partial differential equations. Chin. J. Phys. 43:991-1003. | ||||
|
Younis M (2014a). Soliton solutions of fractional order KdV-Burger's equation. J. Adv. Phys. 4:325-328. Crossref |
||||
|
Younis M (2014b). New exact travelling wave solutions for a class of nonlinear PDEs of fractional order. Math. Sci. Lett. 3:193-197. Crossref |
||||
|
Younis M, Zafar A (2014). Exact solution to nonlinear differential equations of fractional order via -expansion method. Appl. Math. 5:1-6. Crossref |
||||
|
Zayed EME (2009). The -expansion method and its applications to some nonlinear evolution equations in mathematical physics. J. Appl. Math. Comput. 30:89–103. Crossref |
||||
|
Zayed EME, Gepreel KA (2009).The -expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. J. Math. Phys. 50:013502–013513. Crossref |
||||
|
Zayed EME (2011). A note on the modified simple equation method applied to Sharma- Tasso- Olver equation. Appl. Math. Comput. 218:3962–3964. Crossref |
||||
|
Zayed EME, Hoda Ibrahim SA (2012). Exact solutions of nonlinear evolution equation in mathematical physics using the modified simple equation method. Chin. Phys. Lett. 29:060201–4. Crossref |
||||
|
Zayed EME, Arnous AH (2012). Exact solutions of the nonlinear ZK-MEW and the potential YTSF equations using the modified simple equation method. AIP Conf. Proc. 1479:2044–2048. Crossref |
||||
|
Zayed EME, Hoda Ibrahim SA (2013a). The two variable -expansion method for finding exact traveling wave solutions of the (3+1) -dimensional nonlinear Potential Yu-Toda-Sasa-Fukuyama equation. Int. Conf. Adv. Comput. Sci. Electronics Inf. Atlantis Press, pp. 388-392. Crossref |
||||
| Zayed EME, Hoda Ibrahim SA (2013b). Modified simple equation method and its applications for some nonlinear evolution equations in mathematical physics. Int. J. Comput. Appl. 67:39–44. | ||||
|
Zayed EME, Alurrfi KAE (2014a). The -expansion method and its applications to find the exact solutions of nonlinear PDEs for nanobiosciences. Math. Prob. Eng. Article ID 521712: P.10. Crossref |
||||
|
Zayed EME, Alurrfi KAE (2014b). The -expansion method and its applications for solving two higher order nonlinear evolution equations. Math. Prob. Eng. Article ID 746538: P.21. Crossref |
||||
| Zayed EME, Alurrfi KAE (2014c). On solving the nonlinear Schrödinger-Boussinesq equation and the hyperbolic Schrödinger equation by using the -expansion method. Int. J. Phys. Sci. 19:415-429. | ||||
|
Zayed EME, Alurrfi KAE (2014d). The generalized projective Riccati equations method for solving nonlinear evolution equations in mathematical physics. Abst. Appl. Anal. Article ID 259190: P.10. Crossref |
||||
| Zayed EME, Hoda Ibrahim SA (2014). Exact solutions of Kolmogorov-Petrovskii- Piskunov equation using the modified simple equation method. Acta Math. Appl. Sinica. English series. 30:749-754. | ||||
|
Zdravkovic S, Sataric MV, Maluckov A, Balaz A (2014). A nonlinear model of the dynamics of radial dislocations in microtubules. Appl. Math. Comput. 237:227-237. Crossref |
||||
|
Zekovic S, Muniyappan A, Zdravkovic S, Kavitha L (2014). Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules. Chin. Phys. B. 23:020504. Crossref |
||||
|
Zhang GX, Duan YS, Li ZB (2001). Exact solitary wave solutions of nonlinear wave equations. Science China A. 44:396-401. Crossref |
||||
|
Zhang JL, Wang ML, Wang YM, Fang ZD (2006). The improved F-expansion method and its applications. Phys. Lett. A. 350:103–109. Crossref |
||||
|
Zhang S, Tong JL, Wang W (2008). A generalized -expansion method for the mKdv equation with variable coefficients. Phys. Lett. A. 372:2254–2257. Crossref |
||||
| Zhang ZY (2008). New exact traveling wave solutions for the nonlinear Klein-Gordon equation. Turk. J. Phys. 32:235-240. | ||||
|
Zhao XQ, Zhi HY, Zhang HQ (2006).Improved Jacobi elliptic function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system. Chaos Solitons Fractals. 28:112–126. Crossref |
||||
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