A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

References

[1] Liu J. G., Zeng Z. F., He Y. and Ai G. P., A class of exact solution of (3+1)-dimensional generalized shallow water equation system, Int. J. Nonlinear Sci. Numer. Simul. 16 (1) (2015), 43–48.10.1515/ijnsns-2013-0114Search in Google Scholar

[2] Liu J. G. and Zeng Z. F., Multiple soliton solutions, soliton-type solutions and rational solutions for the (3+1)-dimensional potential-YTSF equation, Indian. J. Pure Appl. Math. 45 (2014), 989–1002.10.1007/s13226-014-0100-9Search in Google Scholar

[3] Liu J. G. and Zeng Z. F., Extended generalized hyperbolic-function method and newexact solutions to the generalized Hamiltonian and (2 + 1)-dimensional Nizhnik-Novikov-Veselov equations by the symbolic computation, Fundam. Inf. 132 (2014), 501–517.Search in Google Scholar

[4] Zhang L. and Lin Y. Z., Symbolic computation of exact solutions for nonlinear evolution equations, Nonlinear Dyn. 79 (2) (2015), 823–833.10.1007/s11071-014-1705-6Search in Google Scholar

[5] Liu N., Bäcklund transformation and multi-soliton solutions for the (3+1)-dimensional BKP equation with Bell polynomials and symbolic computation, Nonlinear Dyn. 82 (1-2) (2015), 311–318.10.1007/s11071-015-2159-1Search in Google Scholar

[6] Tang Y. N., Ma W. X. and Xu W., Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation, Chin. Phys. B 21 (2012), 070212.10.1088/1674-1056/21/7/070212Search in Google Scholar

[7] Zhi H. Y., New similarty reduction solutions for the (2+1)-dimensional Nizhnik-Novikov- Veselov equation, Commun. Theor. Phys. 59 (2013), 263–267.10.1088/0253-6102/59/3/03Search in Google Scholar

[8] Moawad S. M., Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations, Phys. Plasm. 22 (2015), 022130.10.1063/1.4913475Search in Google Scholar

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

[10] Hu X. B. and Ma W. X., 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] Woopyo H. and Jung Y. D., 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] Wadati M., Sanuki H. and Konno K., Relationships among inverse method, Bäcklund transformation and an infinite number of conservation laws, Prog. Theor. Phys. 53 (1975), 419–436.10.1143/PTP.53.419Search in Google Scholar

[13] Weis J., Tabor M. and Garnevale G., The painlevé property for partial differential equations, J. Math. Phys. 24 (1983), 522–526.10.1063/1.525721Search in Google Scholar

[14] Yu S. J., Toda K., Sasa N. and Fukuyama T., N-soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3+1) dimensions, J. Phys. A Math. Gen. 31 (1998), 3337–3347.10.1088/0305-4470/31/14/018Search in Google Scholar

[15] Bruzón M. S., Gandarias M. L., Muriel S., Ramíres K., Saez S. and Romero F. R., The Calogero-Bogoyavlenskii-Schiff equation in dimension 2+1 dimensions, Theor. Math. Phys. 137 (1) (2003), 1367–3777.10.1023/A:1026040319977Search in Google Scholar

[16] Calogero F. and Degasperis A., Nonlinear evolution equations solvable by the inverse spectral transform I, Nuovo. Cimento. B 32 (1976), 201–242.10.1007/3-540-08853-9_21Search in Google Scholar

[17] Qawasmeh A. and Alquran M., Soliton and periodic solutions for (2+1)-dimensional dispersive long water-wave system, Appl. Math. Sci. 8 (50) (2014), 2455–2463.10.12988/ams.2014.43170Search in Google Scholar

[18] Alquran M. and Qawasmeh A., Soliton solutions of shallow water wave equations by means of (G′/G)-expansion method, J Appl. Anal. Comput. 4 (3) (2014), 221–229.10.11948/2014010Search in Google Scholar

[19] Qawasmeh A. and Alquran M., Reliable study of some new fifth-order nonlinear equations by means of (G′/G)-expansion method and rational sine-cosine method, Appl. Math. Sci. 8 (120) (2014), 5985–5994.10.12988/ams.2014.48669Search in Google Scholar

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

[21] Zhang Y. W., Solving STO and KD equations with modified Riemann-Liouville derivative using improved (G′/G)-expansion function method, IAENG Int. J. Appl. Math. 45 (1) (2015), 16–22.Search in Google Scholar

[22] Bekir A., 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

[23] Zhang S., Tong J. and Wang W., 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

[24] Zhang J., Wei X. and Lu Y., 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

[25] Date E., M. Jimbo, M. Kashiwara and Miwa T., Transformation groups for soliton equations VI-KP hierarchies of orthogonal and symplectic type, J. Phys. Soc. Japan 50 (1981), 3813–3818.10.1143/JPSJ.50.3813Search in Google Scholar

[26] Date E., Jimbo M., Kashiwara M. and Miwa T., Transformation groups for soliton equations IV-a new hierarchy of soliton equations of KP-type, Phys. D 4 (1981/1982), 343–365.10.1016/0167-2789(82)90041-0Search in Google Scholar

[27] Ma W. X. and Fan E. G., 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

[28] Ma W. X. and Zhu Z. N., 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

[29] Lou S. Y., Dromions, Dromion Lattice, Breathers and Instantons of the Davey-Stewartson Equation, Phys. Scr. 65 (1) (2006), 7–12.10.1238/Physica.Regular.065a00007Search in Google Scholar

[30] Senhadji L. and Shamsollahi M. B., Dromion structures of (2+1)-dimensional sine-Gordon system, Commun. Theor. Phys. 23 (1) (1999), 83–396.Search in Google Scholar