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A new expansion auxiliary equation method for traveling wave solutions of the simplified MCH equation and the ZKBBM equation


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Zayed, E. M. E. (2009). New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G’/G)-expansion method. Journal of Physics A Mathematical and Theoretical, 42(19), 195202. Search in Google Scholar

Zayed, E. M. E., & Gepreel, K. A. (2011). The modified (G’/G)-expansion method and its applications to construct exact solutions for nonlinear PDEs. Wseas transactions on mathematics, 10(8), 270-278. Search in Google Scholar

Akbar, M. A., Ali, N. H. M., & Zayed, E. M. E. (2012). Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G’/G)-expansion method. Communications in Theoretical Physics, 57(2), 173-178. Search in Google Scholar

Naher, H., Abdullah, F. A., & Akbar, M. A. (2012). New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method. Journal of Applied Mathematics, 2012. Search in Google Scholar

Zhao, X., & Tang, D. (2002). A new note on a homogeneous balance method. Physics Letters A, 297(1), 59-67. Search in Google Scholar

Zhao, X., Wang, L., & Sun, W. (2006). The repeated homogeneous balance method and its applications to nonlinear partial differential equations. Chaos, Solitons and Fractals, 28(2), 448-453. Search in Google Scholar

Feng, Z. (2004). Comment on “On the extended applications of homogeneous balance method”. Applied Mathematics and Computation, 158(2), 593-596. Search in Google Scholar

Saied, E. A., El-Rahman, R. G. A., & Ghonamy, M. I. (2009). A generalized Weierstrass elliptic function expansion method for solving some nonlinear partial differential equations. Computers and Mathematics with Applications, 58(9), 1725-1735. Search in Google Scholar

Zayed, E. M. E., & Alurrfi, K. A. E. (2015). A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos, Solitons and Fractals, 78, 148-155. Search in Google Scholar

Yan, Z. (2003). Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey-Stewartson-type equation via a new method. Chaos, Solitons and Fractals, 18(2), 299-309. Search in Google Scholar

Rashidi, M. M., & Erfani, E. (2009). New analytic method for solving Burgers’ and nonlinear heat transfer equations and comparison with HAM. Computer Physics Communications, 180(9), 1539-1544. Search in Google Scholar

Jiwari, R., & Mittal, R. C. (2012). A differential quadrature method for numerical solutions of Burgers-Type equations. International Journal of Numerical Methods for Heat & Fluid Flow, 22(7), 880-895. Search in Google Scholar

Mittal, R. C., & Jiwari, R. (2012). Differential quadrature method for numerical solution of coupled viscous Burgers’ equations. International Journal for Computational Methods in Engineering Science and Mechanics, 13(2), 88-92. Search in Google Scholar

Zhang, H. (2007). Extended Jacobi elliptic function expansion method and its applications. Communications in Nonlinear Science and Numerical Simulation, 12(5), 627-635. Search in Google Scholar

Abdou, M. A. (2007). The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos, Solitons and Fractals, 31(1), 95-104. Search in Google Scholar

Wazwaz, A. M. (2003). A study on nonlinear dispersive partial differential equations of compact and noncompact solutions. Applied Mathematics and Computation, 135(2-3), 399-409. Search in Google Scholar

Fallahzadeh, A., & Shakibi, K. (2015). A method to solve Convection-Diffusion equation based on homotopy analysis method. Journal of Interpolation and Approximation in Scientific Computing, 2015(1), 1-8. Search in Google Scholar

Jawad, A. J. M., Petković, M. D., & Biswas, A. (2010). Modified simple equation method for nonlinear evolution equations. Applied Mathematics and Computation, 217(2), 869-877. Search in Google Scholar

Zayed, E. M. E. (2011). A note on the modified simple equation method applied to Sharma-Tasso-Olver equation. Applied Mathematics and Computation, 218(7), 3962-3964. Search in Google Scholar

Zayed, E. M. E., & Ibrahim, S. A. H. (2012). Exact solutions of nonlinear evolution equations in mathematical physics using the modified simple equation method. Chinese Physics Letters, 29(6), 060201. Search in Google Scholar

Khan, K., Akbar, M. A., & Ali, N. H. M. (2013). The modified simple equation method for exact and solitary wave solutions of nonlinear evolution equation: the GZK-BBM equation and right-handed noncommutative Burgers equations. ISRN Mathematical Physics, 2013. Search in Google Scholar

Zhang, S., & Xia, T. (2007). A generalized new auxiliary equation method and its applications to nonlinear partial differential equations. Physics Letters A, 363(5-6), 356-360. Search in Google Scholar

Fan, E. (2003). A new algebraic method for finding the line soliton solutions and doubly periodic wave solution to a two-dimensional perturbed KdV equation. Chaos, Solitons and Fractals, 15, 567-574. Search in Google Scholar

Zhang, B., Liu, Z., & Mao, J. (2010). New exact solutions for mCH and mDP equations by auxiliary equation method. Applied Mathematics and Computation, 217(4), 1306-1314. Search in Google Scholar

Yuan, W., Meng, F., Huang, Y., et al. (2015). All traveling wave exact solutions of the variant Boussinesq equations. Applied Mathematics and Computation, 268, 865-872. Search in Google Scholar

Yuan, W., Li, Y., Lin, J. (2013). Meromorphic solutions of an auxiliary ordinary differential equation using complex method. Mathematical Methods in the Applied Sciences, 36(13), 1776-1782. Search in Google Scholar

Yuan, W., Huang, Y., & Shang, Y. (2013). All traveling wave exact solutions of two nonlinear physical models. Applied Mathematics and Computation, 219(11), 6212-6223. Search in Google Scholar

Yuan, W., Meng, F., Lin, J., et al. (2016). All meromorphic solutions of an ordinary differential equation and its applications. Mathematical Methods in the Applied Sciences, 39(8), 2083-2092. Search in Google Scholar

Alam, M. N., & Akbar, M. A. (2015). Some new exact traveling wave solutions to the simplified MCH equation and the (1+ 1)-dimensional combined KdV-mKdV equations. Journal of the Association of Arab Universities for Basic and Applied Sciences, 17, 6-13. Search in Google Scholar

Harun-Or-Roshid, Alam, M. N., Akbar, M. A., et al. (2015). Traveling Wave Solutions of the Simplified MCH Equation via Exp (ϕ(ξ)-expansion method. British Journal of Mathematics and Computer Science, 5(5), 595-605. Search in Google Scholar

Shakeel, M., & Mohyud-Din, S. T. (2015). New (G’/G)-expansion method and its application to the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation. Journal of the Association of Arab Universities for Basic and Applied Sciences, 18(1), 66-81.About the Author Search in Google Scholar

eISSN:
2444-8656
Język:
Angielski
Częstotliwość wydawania:
Volume Open
Dziedziny czasopisma:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics