International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

The modified simple equation method for solving nonlinear diffusive predator-prey system and Bogoyavlenskii equations

Elsayed M. E. Zayed
  • Elsayed M. E. Zayed
  • Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt.
  • Google Scholar
Yasser A. Amer
  • Yasser A. Amer
  • Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt.
  • Google Scholar


  •  Received: 08 December 2014
  •  Accepted: 02 February 2015
  •  Published: 28 February 2015

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 (2014a). Traveling wave solutions of the nonlinear (1+1)-dimensional modified Benjamin-Bona-Mahony equation by using novel (G'/G) -expansion method. Phys. Review Res. Int. 4:147-165.
 
Alam MN, Akbar MA (2014b). A new (G'/G) -expansion method and its application to the Burgers equation. Walailak J. Sci. Tech. 11:643-658.
 
Alam MN, Akbar MA (2014c). The new approach of generalized (G'/G) -expansion method for nonlinear evolution equations. Ain Shams Eng. 5(2014):595-603.
Crossref
 
Alam MN, Akbar MA (2014d). Traveling wave solutions for the mKdV equation and the Gardner equation by new approach of the generalized (G'/G)-expansion method, J. Egyptian Math. Society. DOI: 10.1016/j.joems.2014.01.001 (in press).
Crossref
 
Alam MN, Akbar MA, Hoque MF (2014a). 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 (G'/G) -expansion method. Pramana-J. Phys. 83:317-329.
 
Alam MN, Akbar MA, Roshid HO (2014b). Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G) -Expansion Method. Springer Plus. 3:43. doi:10.1186/2193-1801-3-43.
Crossref
 
Alam MN, Akbar MA, Mohyud-Din ST (2014c). General traveling wave solutions of the strain wave equation in microstructured solids via the new approach of generalized (G'/G)-Expansion method. Alexandria Eng. J. 53:233–241.
Crossref
 
Aminikhad H, Moosaei H, Hajipour M (2009). Exact solutions for nonlinear partial differential equations via Exp-function method. Numer. Methods Partial Differ. Equations. 26:1427-1433.
 
Bogoyavlenskii OI (1990). Breaking solitons in 2 + 1 -dimensional integrable equations. Russian Math. Surveys. 45:1-86.
Crossref
 
Clarkson PA, Gordoa PR (1996). A. Pickering, Multicomponent equations associated to non-isospectral scattering problems. Inverse Problems. 13:1463-1476.
Crossref
 
Dai CQ, Zhang JF (2006). Jacobian elliptic function method for nonlinear differential difference equations. Chaos Solutions Fractals. 27:1042-1049.
Crossref
 
Dehghan M, Sabouri M (2013). A Legendre spectral element method on a large spatial domain to solve the predator-prey system modeling interaction populations. Appl. Mathematical Modeling. 37:1028-1038.
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
 
Estevez PG, Prada J (2004). A generalization of the Sine-Gordon equation (2 + 1) - dimensions. J.Nonlinear Math. Phys. 11:168-179.
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
 
Fan E, Zhang H (1998). A note on the homogeneous balance method, Phys. Lett. A. 246:403-406.
Crossref
 
Hafez MG, Alam MN, Akbar MA (2014). Exact traveling wave solutions to the Klein-Gordon equation using the novel -expansion method, Results in Physics (2014).
Crossref
 
He JH (2012). Asymptotic methods for solitary solutions and compactions, Abst. Appl. Anal. Article ID 916793, P. 130.
 
He JH, Wu XH (2006). Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30:700-708.
Crossref
 
Hu MS, Agarwal RP, Yang XJ (2012). Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String. Abstract Appl. Analysis, Article ID 567401, P.15.
 
Jawad AJM, Petkovic MD, Biswas A (2010). Modified simple equation method for nonlinear evolution equations. Appl. Math. Comput. 217: 869-877.
Crossref
 
Kraenkel RA, Manikandan K, Senthivelan M (2013). On certain new exact solutions of a diffusive predator-prey system. Commun. Nonlinear Sci. Numer. Simulat. 18:1269-1274.
Crossref
 
Kudryasho N, Pickering A (1998). Rational solutions for Schwarzian integrable hierarchies. J. Phys. A. 31:9505-9518.
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
 
Malfliet W (1992). Solitary wave solutions of nonlinear wave equation. Am. J. Phys. 60:650-654.
Crossref
 
Malfliet W, Hereman W (1996). The tanh method: Exact solutions of nonlinear evolution and wave equations, Phys. Scr. 54:563-568.
Crossref
 
Petrovskii SV, Malchow H, Li BL (1990). An exact solution of a diffusive predator-prey system. Proc. R. Soc. A. 461:1029-1053.
 
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
 
Wang ML (1998). Exct solutions for a compound KdV-Burgers equation, Phys. Lett. A. 213:279-287.
Crossref
 
Wang ML, Zhang JL, Li XZ (2008). The -expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics. Phys. Lett. A 372:417-423.
Crossref
 
Wazwaz AM (2004a). The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154:714-723.
Crossref
 
Wazwaz (2004b). A sine-cosine method for handling nonlinear wave equations. Math. Comput. Modeling. 40:499-508.
 
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(1996):77-84.
Crossref
 
Yang XJ (2011). Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, Hong Kong.
 
Yang XJ (2012). Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York.
 
Yang XJ, Baleanu D (2012). Fractal heat conduction problem solved by local fractional variation iteration method. Thermal Sci.17:625-628.
Crossref
 
Yang XJ, Srivastava HM, He JH, Baleanu D (2013), Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives. Phys. Lett. A 377:1996-1700.
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 ENE, 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, Hoda Ibrahim SA (2012).  Exact solutions of nonlinear evolution equations in mathematical physics using the modified simple equation method. Chin. Phys. Lett. 29:060201-060204.
Crossref
 
Zayed EME, Hoda Ibrahim SA (2013). Modified simple equation method and its applications for some nonlinear evolution equations in mathematical physics. Int. J. Comput. Appl. 67:39-44.
 
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.
 
Zhang JL, Wang ML, Wang YM, Fang ZD (2006). The improved F- expansion method and its applications, Phys. Lett. A. 350:103-109.
 
Zhang ZY (2008). New exact traveling wave solutions for the nonlinear Klein-Gordon equation. Turk. J. Phys. 32:235-240.
 
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
 
Zhao XO, Zhi HY, Zhang HO (2006). Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system. Chaos Solitons Fractals. 28:112-126.
Crossref