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Exact solutions of a coupled Boussinesq equation. (English) Zbl 1331.35309

Cojocaru, Monica G. (ed.) et al., Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26–30, 2013. Cham: Springer (ISBN 978-3-319-12306-6/hbk; 978-3-319-12307-3/ebook). Springer Proceedings in Mathematics & Statistics 117, 323-327 (2015).
Summary: In this chapter, \((G'/G)\)-expansion method is employed to derive new exact solutions of a coupled Boussinesq equation. Three types of solutions are obtained, namely, hyperbolic function solutions, trigonometric function solutions and rational solutions. These solutions are travelling wave solutions.
For the entire collection see [Zbl 1325.00049].

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
35C07 Traveling wave solutions
35C09 Trigonometric solutions to PDEs
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[1] Ablowitz, M. J.; Clarkson, P. A., Soliton, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge: Cambridge University Press, Cambridge · Zbl 0762.35001 · doi:10.1017/CBO9780511623998
[2] Gu, C. H., Soliton Theory and Its Application (1990), Zhejiang: Zhejiang Science and Technology Press, Zhejiang
[3] Matveev, V. B.; Salle, M. A., Darboux Transformation and Soliton (1991), Berlin: Springer-Verlag, Berlin · Zbl 0744.35045 · doi:10.1007/978-3-662-00922-2
[4] Hirota, R., The Direct Method in Soliton Theory (2004), Cambridge: Cambridge University Press, Cambridge · Zbl 1099.35111 · doi:10.1017/CBO9780511543043
[5] Wang, M.; Xiangzheng, L. X.; Jinliang, Z. J., The \((G'/G)\) -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett., A372, 417-423 (2008) · Zbl 1217.76023 · doi:10.1016/j.physleta.2007.07.051
[6] Yan, Z. Y., A reduction mKdV method with symbolic computation to construct new doubly-periodic solutions for nonlinear wave equations, Int. J. Mod. Phys. C., 14, 661-672 (2003) · Zbl 1082.35518 · doi:10.1142/S0129183103004814
[7] Wazwaz, M., The tanh and sine-cosine method for compact and noncompact solutions of nonlinear Klein Gordon equation, Appl. Math. Comput., 167, 1179-1195 (2005) · Zbl 1082.65584 · doi:10.1016/j.amc.2004.08.006
[8] Lu, D. C., Jacobi elliptic functions solutions for two variant Boussinesq equations, Chaos Soliton Fract., 24, 1373-1385 (2005) · Zbl 1072.35567 · doi:10.1016/j.chaos.2004.09.085
[9] Yan, Z. Y., Abundant families of Jacobi elliptic functions of the (2+1) dimensional integrable Davey-Stewartson-type equation via a new method, Chaos Soliton Fract., 18, 299-309 (2003) · Zbl 1069.37060 · doi:10.1016/S0960-0779(02)00653-7
[10] Wang, M.; Li, X., Extended F-expansion and periodic wave solutions for the generalized Zakharov equations, Phys. Lett. A., 343, 48-54 (2005) · Zbl 1181.35255 · doi:10.1016/j.physleta.2005.05.085
[11] He, J. H.; Wu, X. H., Exp-function method for nonlinear wave equations, Chaos Soliton Fract., 30, 7-0 (2006)
[12] Bluman, G. W.; Kumei, S., Symmetries and Differential Equations (1989), New York: Springer-Verlag, New York · Zbl 0698.35001 · doi:10.1007/978-1-4757-4307-4
[13] Olver, P.J.: Applications of Lie Groups to Differential Equations (Graduate Texts in Mathematics) vol. 107, 2nd edn. Springer-Verlag, Berlin (1993) · Zbl 0785.58003
[14] Ibragimov, N.H.: CRC Handbook of Lie Group Analysis of Differential Equations, Vol 1-3. CRC Press, Boca Raton (1994-1996) · Zbl 0864.35001
[15] Ovsiannikov, L. V., Group Analysis of Differential Equations (1982), New York: Academic, New York · Zbl 0485.58002
[16] Wazwaz, A. M., Solitons and periodic wave solutions for couples nonlinear equations, Int. J. Nonlinear Sci., 14, 266-277 (2012) · Zbl 1394.35448
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