Multiple Soliton Solutions, Soliton-Type Solutions and Hyperbolic Solutions for the Benjamin–Bona–Mahony Equation with Variable Coefficients in Rotating Fluids and One-Dimensional Transmitted Waves

References

[1] J. G. Liu, Y. Z. Li, and G. M. Wei, Auto-Bäcklund transformation and soliton-typed solutions of the generalized variable-coefficient KP equation (in Chinese), Chin. Phys. Lett. 23 (2006), 1670–1673.10.1088/0256-307X/23/7/004Search in Google Scholar

[2] M. G. Asaad and W. X. Ma, Pfaffian solutions to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation and its modified counterpart, Appl. Math. Comput. 218 (2012), 5524–5542.10.1016/j.amc.2011.11.042Search in Google Scholar

[3] M. G. Asaad and W. X. Ma, Extended gram-type determinant, wave and rational solutions to two (3+1)-dimensional nonlinear evolution equations, Appl. Math. Comput. 219 (2012), 213–225.10.1016/j.amc.2012.06.007Search in Google Scholar

[4] W. X. Ma and Z. N. Zhu, Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm, Appl. Math. Comput. 218 (2012), 11871–11879.10.1016/j.amc.2012.05.049Search in Google Scholar

[5] W. X. Ma, Y. Zhang, Y. N. Tang, and J. Y. Tu, Hirota bilinear equations with linear subspaces of solutions, Appl. Math. Comput. 218 (2012), 7174–7183.10.1016/j.amc.2011.12.085Search in Google Scholar

[6] A. M. Wazwaz, Four (2+1)-dimensional integrable extensions of the Kadomtsev-Petviashvili equation, Appl. Math. Comput. 215 (2010), 3631–3644.10.1016/j.amc.2009.11.001Search in Google Scholar

[7] W. X. Ma and E. G. Fan, Linear superposition principle applying to Hirota bilinear equations, Commun. Theor. Phys. 61 (2011), 950–959.10.1016/j.camwa.2010.12.043Search in Google Scholar

[8] A. M. Wazwaz, N-soliton solutions for shallow water waves equations in (1+1) and (2+1) dimensions, Appl. Math. Comput. 217 (2011), 8840–8845.10.1016/j.amc.2011.03.048Search in Google Scholar

[9] C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for solving the Korteweg-De Vries equation, Phys. Rev. Lett. 19 (1967), 1095–1097.10.1103/PhysRevLett.19.1095Search in Google Scholar

[10] X. B. Hu and W. X. Ma, Application of Hirota’s bilinear formalism to the Toeplitz lattice-some special soliton- like solutions, Phys. Lett. A 293 (2002), 161–165.10.1016/S0375-9601(01)00850-7Search in Google Scholar

[11] H. Woopyo and Y. D. Jung, Auto-Bäcklund transformation and analytic solutions for general variable-coefficient KdV equation, Phys. Lett. A 257 (1999), 149–152.10.1016/S0375-9601(99)00322-9Search in Google Scholar

[12] T. B. Benjamin, J. L. Bona, and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems, Trans. Roy. Soc. (Lond.) Ser. A 272 (1992), 47–78.10.1098/rsta.1972.0032Search in Google Scholar

[13] D. J. Korteweg and G. de Vries, On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves, Philos. Mag. 39 (1895), 422–443.10.1080/14786449508620739Search in Google Scholar

[14] J. Meiss and W. Horton, Fluctuation spectra of drift wave soliton gas, Phys. Fluid. 25 (1982), 1838–1843.10.1063/1.863662Search in Google Scholar

[15] C. Yan, Regularized long wave equation and inverse scattering transform, J. Math. Phys. 24 (1993), 2618–2630.10.1063/1.530087Search in Google Scholar

[16] P. J. Olver, Applications of Lie groups to differential equations, New York: Springer-Verlag, 1993.10.1007/978-1-4612-4350-2Search in Google Scholar

[17] K. Singh, R. K. Gupta, and S. Kumar, Benjamin-Bona-Mahony (BBM) equation with variable coefficients: Similarity reductions and Painlevé analysis, Appl. Math. Comput. 217 (2011), 7021–7027.10.1016/j.amc.2011.02.003Search in Google Scholar

[18] A. Bekir, Application of the (G'/G) expansion method for nonlinear evolution equations, Phys. Lett. A 372 (2008), 3400–3406.10.1016/j.physleta.2008.01.057Search in Google Scholar

[19] M. Wang, X. Li, and J. Zhang, The (G'/G) expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A. 372 (2008), 417–423.10.1016/j.physleta.2007.07.051Search in Google Scholar

[20] E. M. E. Zayed and K. A. Gepreel, The (G'/G) expansion method for finding traveling wave solutions of nonlinear PDEs in mathematical physics, J. Math. Phys. 50 (2009), 13502–13513.10.1063/1.3033750Search in Google Scholar

[21] E. M. E. Zayed, The (G'/G) expansion method and its applications to some nonlinear evolution equations in the mathematical physics, J. Appl. Math. Comput. 31 (2009), 89–103.10.1007/s12190-008-0159-8Search in Google Scholar

[22] S. Zhang, J. Tong, and W. Wang, A generalized (G'/G) expansion method for the mKdV equation with variable coefficients, Phys. Lett. A 372 (2008), 2254–2257.10.1016/j.physleta.2007.11.026Search in Google Scholar

[23] J. Zhang, X. Wei, and Y. Lu, A generalized (G'/G) expansion method and its applications, Phys. Lett. A 372 (2008), 3653–3658.10.1016/j.physleta.2008.02.027Search in Google Scholar

[24] Y. M. Chen, S. H. Ma, and Z. Y. Ma, New exact solutions of a (3+1)-dimensional Jimbo-Miwa system, Chin. Phys. B 22 (2013), 050510.10.1088/1674-1056/22/5/050510Search in Google Scholar

[25] C. L. Zheng, J. F. Zhang, and G. Solution, Fractal localized structures for the (2+1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system, Chin. Phys. Lett. 19 (2002), 1399–1402.10.1088/0256-307X/19/10/301Search in Google Scholar

[26] J. F. Zhang and X. J. Lai, New variable separated solutions and ghoston structure for the (2+1)-dimensional sine-Gordon system, Chin. Phys. Lett. 21 (2004), 1449–1452.10.1088/0256-307X/21/8/010Search in Google Scholar

[27] J. F. Zhang, C. L. Zheng, J. P. Meng, and J. P. Fang, Chaotic dynamical behaviour in soliton solutions for a new (2+1)-dimensional long dispersive wave system, Chin. Phys. Lett. 20 (2003), 448–451.10.1088/0256-307X/20/4/302Search in Google Scholar

[28] C. L. Zheng, J. F. Zhang, W. H. Huang, and L. Q. Chen, Peakon and Foldon excitations in a (2+1)-dimensional breaking soliton system, Chin. Phys. Lett. 20 (2003), 783–786.10.1088/0256-307X/20/6/301Search in Google Scholar

[29] M. J. Ablowitz and H. Segur, Solitons and the inverse scattering transform, Society for Industrial and Applied Mathematics, Philadelphia, 1981.10.1137/1.9781611970883Search in Google Scholar