Modified Double Sub-equation Method for Finding Complexiton Solutions to the ( $$1+1$$ 1 + 1 ) Dimensional Nonlinear Evolution Equations
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ablowitz, M.J., Clarkson, P.A.: Soliton, Nonlinear Evolution Equations and Inverse Scatting. Cambridge University Press, New York (1991)
Ma, W.X.: Travelling wave solutions to a seventh order generalized KdV equation. Phys. Lett. A 180, 221–224 (1993)
Ma, W.X., Zhou, D.T.: Solitary wave solutions to a generalized KdV equation. Acta Phys. Sin. 42, 1731–1734 (1993)
Wang, M.L., Zhou, Y.B., Li, Z.B.: Applications of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A 216, 67–75 (1996)
Zhu, Z.N.: Lax pair, Bäcklund transformation, solitary wave solution and finite conservation laws of the general KP equation and MKP equation with variable coefficients. Phys. Lett. A 180, 409–412 (1993)
Ma, W.X., Fuchssteiner, B.: Explicit and exact solutions to a Kolmogorov–Petrovskii–Piskunov equation. Int. J. Non-Linear Mech. 31, 329–338 (1996)
Tibor, B., Bèla, L., Csaba, M., Zsolt, U.: The hyperbolic tangent distribution family. Powder Technol. 97, 100–108 (1998)
Wang, M., Li, X., Zhang, J.: The $$({G}^{\prime }/G)$$ ( G ′ / G ) -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372, 417–423 (2008)
Roshid, H.O., Alam, M.N., Hoque, M.F., Akbar, M.A.: A new extended $$({G}^{\prime }/G)$$ ( G ′ / G ) -expansion method to find exact traveling wave solutions of nonlinear evolution equations. Math. Stat. 1, 162–166 (2013)
Ma, W.X., Huang, T., Zhang, Y.: A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr. 82, 065003 (2010)
Fu, Z.T., Liu, S.K., Liu, S.D., Zhao, Q.: New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Phys. Lett. A 290, 72–76 (2001)
Chen, H.T., Zhang, H.Q.: Improved Jacobin elliptic function method and its applications. Chaos Solitons Fractals 15, 585–591 (2003)
Chen, H.T., Zhang, H.Q.: New multiple soliton-like solutions to the Generalized (2 + 1)-dimensional KP equation. Appl. Math. Comput. 157, 765–773 (2004)
Chen, H.T., Zhang, H.Q.: New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation. Chaos Solitons Fractals 20, 765–769 (2004)
Fan, E.G.: Extanded tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277, 212–218 (2000)
Zhang, S.: A generalized auxiliary equation method and its application to (2+1)-dimensional Korteweg-de Vries equations. Comput. Math. Appl. 54, 1028–1038 (2007)
Chen, Y., Wang, Q.: Multiple Riccati equations rational expansion method and complexiton solutions of the Whitham–Broer–Kaup equation. Phys. Lett. A 347, 215–227 (2005)
Chen, H.T., Yang, S.H., Ma, W.X.: Double sub-equation method for complexiton solutions of nonlinear partial differential equations. Appl. Math. Comput. 219(9), 4775–4781 (2013)
Lou, S.Y., Hu, H.C., Tang, X.Y.: Interactions among periodic waves and solitary waves of the (N+1)-dimensional sine-Gordon field. Phys. Rev. E 71, 036604 (2005)
Kutluay, S., Bahadir, A.R., Ozdes, A.: Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit finite difference methods. J. Comput. Appl. Math. 103, 251–261 (1999)
Biazar, J., Aminikhah, H.: Exact and numerical solutions for non-linear Burger’s equationby VIM. Math. Comput. Model. 49, 1394–1400 (2009)
Hepson, O.E.: Numerical solutions of the Gardner equation by extended form of the cubic B-splines. arXiv:1702.02776v1 [math.NA] 9 Feb 2017
Wazwaz, A.M.: New solitons and kink solutions for the Gardner equation. Commun. Nonlinear Sci. Numer. Simul. 12(8), 1395–1404 (2007)
Ruderman, M.S., Talipova, T., Pelinovsky, E.: Dynamics of modulationally unstable ion-acoustic wavepackets in plasmas with negative ions. J. Plasma Phys. 74(05), 639–656 (2008)
Kamchatnov, A.M., Kuo, Y.H., Lin, T.C., Horng, T.L., Gou, S.C., Clift, R., El, G.A., Grimshaw, R.H.: Undular bore theory for the Gardner equation. Phys. Rev. E 86(3), 036605 (2012)
Kumar, S., Kumar, A., Baleanu, D.: Two analytical methods for time-fractional nonlinear coupled Boussinesq–Burger’s equations arise in propagation of shallow water waves. Nonlinear Dyn. 85(2), 699–715 (2016)
Çenesiz, Y., Baleanu, D., Kurt, A., Tasbozan, O.: New exact solutions of Burgers’ type equations with conformable derivative. Waves Random Complex Media 27(1), 103–116 (2017)