The (G′/G)-expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines

References

• Ablowitz MJ, Clarkson PA. Solitons, nonlinear evolution equations and inverse scattering transform. New York (NY, USA): Cambridge University Press; 1991.
   Google Scholar
• Hirota R. Exact solutions of the KdV equation for multiple collisions of solutions. Phys Rev Lett. 1971;27:1192–1194. doi: 10.1103/PhysRevLett.27.1192
   Web of Science ®Google Scholar
• Weiss J, Tabor M, Carnevale G. The Painlevé property for partial differential equations. J. Math. Phys. 1983;24:522–526. doi: 10.1063/1.525721
   Web of Science ®Google Scholar
• Kudryashov NA. On types of nonlinear nonintegrable equations with exact solutions. Phys Lett A. 1991;155:269–275. doi: 10.1016/0375-9601(91)90481-M
   Web of Science ®Google Scholar
• Rogers C, Shadwick WF. Bäcklund transformations and their applications. New York (NY): Academic Press; 1982.
   Google Scholar
• Zayed EM, Alurrfi KA. The Bäcklund transformation of the Riccati equation and its applications to the generalized KdV-mKdV equation with any-order nonlinear terms. PanAmerican Math. J. 2016;26:50–62.
   Google Scholar
• EL-Wakil SA, Madkour MA, Abdou MA. Application of exp-function method for nonlinear evolution equations with variable coefficients. Phys Lett A. 2007;369:62–69. doi: 10.1016/j.physleta.2007.04.075
   Web of Science ®Google Scholar
• Wang YP. Solving the (3+1)-dimensional potential-YTSF equation with Exp-function method 2007 ISDN. J. Phys. Conf. Ser. 2008;96:012186. doi: 10.1088/1742-6596/96/1/012186
   Google Scholar
• Khan K, Akbar MA. Traveling wave solutions of the (2+1)-dimensional Zoomeron equation and the Burgers equations via the MSE method and the Exp-function method. Ain Shams Eng. J. 2014;5:247–256. doi: 10.1016/j.asej.2013.07.007
   Google Scholar
• Fan EG. Extended tanh-function method and its applications to nonlinear equations. Phys Lett A. 2000;277:212–218. doi: 10.1016/S0375-9601(00)00725-8
   Web of Science ®Google Scholar
• Zhang S, Xia TC. A further improved tanh-function method exactly solving the (2+1)-dimensional dispersive long wave equations. Appl. Math. E-Notes. 2008;8:58–66.
   Google Scholar
• Zayed EM, Alurrfi KA. On solving the nonlinear Biswas-Milovic equation with dual-power law nonlinearity using the extended tanh-function method. J Adv. Phys. 2015;11:3001–3012.
   Google Scholar
• Zheng B, Feng Q. The Jacobi elliptic equation method for solving fractional partial differential equations. Abs. Appl. Anal. 2014; Article ID 249071:9 pages.
   Google Scholar
• Hong-cai MA, Zhang ZP, Deng A. A new periodic solution to Jacobi elliptic functions of MKdV equation and BBM equation. Acta Math. Appl. Sinica. English series, 2012;28:409–415. doi: 10.1007/s10255-012-0153-7
   Web of Science ®Google Scholar
• Zayed EM, Alurrfi KA. A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos Solitons Fractals. 2015;78:148–155. doi: 10.1016/j.chaos.2015.07.018
   Web of Science ®Google Scholar
• Wang M, Li X, Zhang J. The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys Lett A. 2008;372:417–423. doi: 10.1016/j.physleta.2007.07.051
   Web of Science ®Google Scholar
• Li ZL. Constructing of new exact solutions to the GKdV-mKdV equation with any-order nonlinear terms by (G'/G)-expansion method. Appl. Math. Comput. 2010;217:1398–1403.
   Web of Science ®Google Scholar
• Zayed EM. The (G'/G)-expansion method and its applications to some nonlinear evolution equations in the mathematical physics. J. Appl. Math. Comput. 2009;30:89–103. doi: 10.1007/s12190-008-0159-8
   Google Scholar
• Zayed EM. The (G'/G)-expansion method combined with the Riccati equation for finding exact solutions of nonlinear PDEs. J. Appl. Math. Inform. 2011;29:351–367.
   Google Scholar
• Zayed EM, Alurrfi KA. Extended generalized (G'/G)-expansion method for solving the nonlinear quantum Zakharov Kuznetsov equation. Ricerche Mat. 2016;65:235–254. doi: 10.1007/s11587-016-0276-x
   Web of Science ®Google Scholar
• Li Lx, Li QE, Wang M. The (G/G',1/G)-expansion method and its application to traveling wave solutions of the Zakharov equations. Appl. Math. J. Chin. Uni. 2010;25:454–462. doi: 10.1007/s11766-010-2128-x
   Google Scholar
• Zayed EM, Alurrfi KA. On solving two higher-order nonlinear PDEs describing the propagation of optical pulses in optic fibers using the (G/G',1/G)-expansion method. Ricerche Mat. 2015;64:164–194. doi: 10.1007/s11587-015-0226-z
   Web of Science ®Google Scholar
• Zayed EM, Shahoot AM, Alurrfi KA. The (G/G',1/G)-expansion method and its applications for constructing many new exact solutions of the higher-order nonlinear Schrödinger equation and the quantum Zakharov–Kuznetsov equation. Opt. Quant. Electron. 2018;50. doi: 10.1007/s11082-018-1337-z
   Web of Science ®Google Scholar
• Yan ZY. Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres. Chaos Solitons Fractals. 2003;16:759–766. doi: 10.1016/S0960-0779(02)00435-6
   Web of Science ®Google Scholar
• Zayed EM, Alurrfi KA. The generalized projective Riccati equations method and its applications for solving two nonlinear PDEs describing microtubules. Int. J. Phys. Sci. 2015;10:391–402. doi: 10.5897/IJPS2015.4289
   Google Scholar
• Shahoot AM, Alurrfi KA, Hassan IM, et al. Solitons and other exact solutions for two nonlinear PDEs in mathematical physics using the generalized projective Riccati equations method. Adv. Math. Phys. 2018; (In press).
   Web of Science ®Google Scholar
• Abdoulkary S, Beda T, Dafounamssou O, et al. Dynamics of solitary pulses in the nonlinear low-pass electrical transmission lines through the auxiliary equation method. J. Mod. Phys. Appl. 2013;2:69–87.
   Google Scholar