Application of the Exp (−φ(ζ))-expansion method for solitary wave solutions

References

• Abbasbandy, S. (2007). Numerical solutions of nonlinear Klein-Gordon equation by variational iteration method. International Journal for Numerical Methods in Engineering, 70(7), 876–881. doi: 10.1002/nme.1924
   Web of Science ®Google Scholar
• Abdou, M. A. (2007). The extended tanh-method and its applications for solving nonlinear physical models. Applied Mathematics and Computation, 190(1), 988–996. doi: 10.1016/j.amc.2007.01.070
   Web of Science ®Google Scholar
• Akbar, M. A., & Ali, N. H. M. (2012). New Solitary and Periodic Solutions of Nonlinear Evolution Equation by Exp-function Method. World Applied Sciences Journal, 17(12), 1603–1610.
   Google Scholar
• Akbar, M. A., Ali, N. H. M., & Zayed, E. M. E. (2012). Abundant exact traveling wave solutions of the generalized Bretherton equation via (G′/G)-expansion method. Communications in Theoretical Physics, 57(2), 173–178. doi: 10.1088/0253-6102/57/2/01
   Google Scholar
• Ali, A. T. (2011). New generalized Jacobi elliptic function rational expansion method. Journal of Computational and Applied Mathematics, 235(14), 4117–4127. doi: 10.1016/j.cam.2011.03.002
   Web of Science ®Google Scholar
• Dai, C. Q., Wang, Y. Y., Fan, Y., & Yu, D. G. (2018). Reconstruction of stability for Gaussian spatial solitons in quintic–septimal nonlinear materials under PT -symmetric potentials. Nonlinear Dynamics, 92(3), 1351–1358. doi: 10.1007/s11071-018-4130-4
   Web of Science ®Google Scholar
• Ding, D. J., Jin, D. Q., & Dai, C. Q. (2017). Analytical solutions of differential difference Sine- Gordon equation. Thermal Science, 21(4), 1701–1705. doi: 10.2298/TSCI160809056D
   Web of Science ®Google Scholar
• Feng, G., Yang, X. J., & Srivastava, H. M. (2017). Exact Travelling wave solutions for linear and nonlinear heat transfer equations. Thermal Science, 21(6), 2307–2311. doi: 10.2298/TSCI161013321G
   Google Scholar
• He, J. H., & Wu, X. H. (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30, 700–708. doi: 10.1016/j.chaos.2006.03.020
   Web of Science ®Google Scholar
• Hirota, R. (1973). Exact envelope soliton solutions of a nonlinear wave equation. Journal of Mathematical Physics, 14(7), 805–810. doi: 10.1063/1.1666399
   Web of Science ®Google Scholar
• Hirota, R., & Satsuma, J. (1981). Soliton solution of a coupled KdV equation. Physics Letters A, 85(8–9), 407–408. doi: 10.1016/0375-9601(81)90423-0
   Web of Science ®Google Scholar
• Hu, H., & Li, Y. (2018). New interaction solutions and nonlocal symmetries for the (2 + 1)-dimensional coupled Burgers equation. Arab Journal of Basic and Applied Sciences, 25(2), 71–76. doi: 10.1080/25765299.2018.1449417
   Google Scholar
• Inc, M., & Evans, D. J. (2004). On travelling wave solutions of some nonlinear evolution Equations. International Journal of Computer Mathematics, 81(2), 191–202. doi: 10.1080/00207160310001603307
   Web of Science ®Google Scholar
• Islam, M. T., Akbar, M. A., & Azad, M. A. K. (2017). Multiple closed form wave solutions to the KdV and modified KdV equations through the rational (G′/G)-expansion method. Journal of the Association of Arab Universities for Basic and Applied Sciences, 24(1), 160–168. doi: 10.1016/j.jaubas.2017.06.004
   Google Scholar
• Khan, K., & Akbar, M. A. (2013). Application of   exp ⁡(−φξ)-expansion Method to find the Exact Solutions of Modified Benjamin-Bona-Mahony Equation. World Applied Sciences Journal, 24(10), 1373–1377.
   Google Scholar
• Kaplan, M., & Akbulut, A. (2018). Application of two different algorithms to the approximate long water wave equation with conformable fractional derivative. Arab Journal of Basic and Applied Sciences, 25(2), 77–84. doi: 10.1080/25765299.2018.1449348
   Google Scholar
• Liping, W., Senfa, C., & Chunping, P. (2009). Travelling wave solution for Generalized Drinfeld-Sokolov equations. Applied Mathematical Modelling, 33, 4126–4130.
   Google Scholar
• Saad, K. M., Al-Shareef, E. H., Mohamed, M. S., & Yang, X. J. (2017). Optimal q-homotopy analysis method for time-space fractional gas dynamics equation. The European Physical Journal Plus, 132(1), 11303–11306. doi: 10.1140/epjp/i2017-11303-6
   Web of Science ®Google Scholar
• Shehata, A. R. (2010). The travelling wave solutions of the perturbed nonlinear Schrodinger equation and the cubic-quintic Ginzburg Landau equation using the modified (G′/G)-expansion method. Applied Mathematics and Computation, 217(1), 1–10. doi: 10.1016/j.amc.2010.03.047
   Google Scholar
• Sirendaoreji. (2004). New exact travelling wave solutions for the Kawahara and modified Kawahara equations. Chaos, Solitons & Fractals, 19, 147–150.
   Web of Science ®Google Scholar
• Wang, M. (1995). Solitary wave solutions for variant Boussinesq equations. Physics Letters A, 199(3–4), 169–172. doi: 10.1016/0375-9601(95)00092-H
   Web of Science ®Google Scholar
• Wang, M., Li, X., & Zhang, J. (2008). The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372(4), 417–423. doi: 10.1016/j.physleta.2007.07.051
   Web of Science ®Google Scholar
• Wang, Y. Y., Chen, L., Dai, C. Q., Zheng, J., & Fan, Y. (2017). Exact vector multipole and vortex solitons in the media with spatially modulated cubic–quintic nonlinearity. Nonlinear Dynamics, 90(2), 1269–1275. doi: 10.1007/s11071-017-3725-5
   Web of Science ®Google Scholar
• Wang, Y. Y., Dai, C. Q., Xu, Y., Q., Zheng, J., & Fan, Y. (2018). Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrödinger equation. Nonlinear Dynamics, 92(3), 1261–1269. doi: 10.1007/s11071-018-4123-3
   Web of Science ®Google Scholar
• Wang, Y. Y., Zhang, Y. P., & Dai, C. Q. (2016). Re-study on localized structures based on variable separation solutions from the modified tanh-function method. Nonlinear Dynamics, 83(3), 1331–1339. doi: 10.1007/s11071-015-2406-5
   Web of Science ®Google Scholar
• Wazwaz, A. M. (2004). A sine-cosine method for handing nonlinear wave equations. Mathematical and Computer Modeling, 40(5-6), 499–508. doi: 10.1016/j.mcm.2003.12.010
   Google Scholar
• Weiss, J., Tabor, M., & Carnevale, G. (1983). The Painleve property for partial differential equations. Journal of Mathematical Physics, 24(3), 522–526. doi: 10.1063/1.525721
   Web of Science ®Google Scholar
• Yang, X. J. (2016). A New integral transform method for solving steady Heat transfer problem. Thermal Science, 20(suppl. 3), 639–S642. doi: 10.2298/TSCI16S3639Y
   Google Scholar
• Yang, X. J., & Feng, G. (2017). A New Technology for Solving Diffusion and Heat Equations. Thermal Science, 21(1 Part A), 133–140. doi: 10.2298/TSCI160411246Y
   Web of Science ®Google Scholar
• Yang, X. J., Feng, G., & Srivastava, H. M. (2017). Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations. Computers & Mathematics with Applications, 73(2), 203–210. doi: 10.1016/j.camwa.2016.11.012
   Web of Science ®Google Scholar
• Yang, X. J., Tenreiro Machado, J. A., Baleanu, D., & Cattani, C. (2016). On exact traveling wave solutions for local fractional Korteweg-de Vries equation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(8), 084312. doi: 10.1063/1.4960543
   PubMed Web of Science ®Google Scholar
• Zayed, E. M. E. (2010). Traveling wave solutions for higher dimensional nonlinear evolution equations using the (G′/G)-expansion method. Journal of Applied Mathematics & Informatics, 28, 383–395.
   Google Scholar
• Zayed, E. M. E., & Gepreel, K. A. (2009). The (G′/G)-expansion method for finding the traveling wave solutions of nonlinear partial differential equations in mathematical physics. Journal of Mathematical Physics, 50, (1), 013502–013514. doi: 10.1063/1.3033750
   Google Scholar
• Zayed, E. M. E., & Al-Nowehy, A. G. (2017). The solitary wave ansatz method for finding the exact bright and dark soliton solutions of two nonlinear Schrödinger equations. Journal of the Association of Arab Universities for Basic and Applied Sciences, 24(1), 184–190. doi: 10.1016/j.jaubas.2016.09.003
   Google Scholar
• Zayed, E. M. E., Zedan, H. A., & Gepreel, K. A. (2004). On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV equations. Chaos, Solitons & Fractals, 22, 285–303. doi: 10.1016/j.chaos.2003.12.045
   Web of Science ®Google Scholar
• Zhang, J., Jiang, F., & Zhao, X. (2010). An improved (G′/G)-expansion method for solving nonlinear evolution equations. International Journal of Computer Mathematics, 87(8), 1716–1725. doi: 10.1080/00207160802450166
   Web of Science ®Google Scholar
• Zhang, F., Qi, J. M., & Yuan, W. J. (2013). Further Results about Traveling Wave Exact Solutions of the Drinfeld-Sokolov Equations. Journal of Applied Mathematics, 2013, 1–6. doi: 10.1155/2013/523732
   Google Scholar