Exact solitary wave and quasi-periodic wave solutions of the KdV-Sawada-Kotera-Ramani equation

Li, JB, Zhang, Y: Homoclinic manifolds, center manifolds and exact solutions of four-dimensional traveling wave systems for two classes of nonlinear wave equations. Int. J. Bifurc. Chaos 21(2), 527-543 (2011)

Yang, J: Dynamics of embedded solitons in the extended Korteweg-de Vries equations. Stud. Appl. Math. 106, 337-365 (2001)

Inc, M, Kilic, B: Classification of traveling wave solutions for time-fractional fifth-order KdV-like equation. Waves Random Complex Media 24(2), 393-403 (2014)

Inc, M: Some special structures for the generalized nonlinear Schrödinger equation with nonlinear dispersion. Waves Random Complex Media 23(2), 77-88 (2013)

Kilic, B, Inc, M: The first integral method for the time fractional Kaup-Boussinesq system with time dependent coefficient. Appl. Math. Comput. 254, 70-74 (2015)

Ma, WX, Lee, JH: A transformed rational function method and exact solutions to the ( 3 + 1 ) $(3+1)$ -dimensional Jimbo-Miwa equation. Chaos Solitons Fractals 42(3), 1356-1363 (2009)

Zhang, S, Xia, T: A generalized new auxiliary equation method and its applications to nonlinear partial differential equations. Phys. Lett. A 363, 356-360 (2007)

Li, H, Wang, KM, Li, JB: Exact traveling wave solutions for the Benjamin-Bona-Mahony equation by improved Fan sub-equation method. Appl. Math. Model. 37, 7644-7652 (2013)

Parkes, EJ, Duffy, BR, Abbott, PC: The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations. Phys. Lett. A 295, 280-286 (2002)

Feng, DH, Li, KZ: Exact traveling wave solutions for a generalized Hirota-Satsuma coupled KdV equation by Fan sub-equation method. Phys. Lett. A 375, 2201-2210 (2011)

Fan, E: Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics. Chaos Solitons Fractals 16, 819-839 (2003)

Fan, E: Supersymmetric KdV-Sawada-Kotera-Ramani equation and its quasi-periodic wave solutions. Phys. Lett. A 374, 744-749 (2010)

Hirota, R, Ito, M: Resonance of solitons in one dimension. J. Phys. Soc. Jpn. 52(3), 744-748 (1983)

Konno, K: Conservation laws of modified Sawada-Kotera equation in complex plane. J. Phys. Soc. Jpn. 61, 51-54 (1992)

Zhang, J, Zhang, J, Bo, L: Abundant travelling wave solutions for KdV-Sawada-Kotera equation with symbolic computation. Appl. Math. Comput. 203, 233-237 (2008)

Qin, Z, Mu, G, Ma, H: G ′ / G $G'/G$ -Expansion method for the fifth-order forms of KdV-Sawada-Kotera equation. Appl. Math. Comput. 222, 29-33 (2013)

Champneys, AR, Groves, MD, Woods, PD: A global characterization of gap solitary wave solutions to a coupled KdV system. Phys. Lett. A 271, 178-190 (2000)

Champneys, AR, Malomed, BA, Yang, J, Kaup, DJ: Embedded solitons: solitary wave in resonance with the linear spectrum. Physica D 152, 340-354 (2001)

Yang, J, Malomed, BA, Kaup, DJ, Champneys, AR: Embedded solitons: a new type of solitary wave. Math. Comput. Simul. 56, 585-600 (2001)

Yagasaki, K, Wagenknecht, T: Detection of symmetric homoclinic orbits to saddle-centres in reversible systems. Physica D 214, 169-181 (2006)

Cosgrove, MC: Higher-order Painlevé equations in the polynomial class I. Bureau symbol P2. Stud. Appl. Math. 104, 1-65 (2000)

Zhang, LJ, Khalique, CM: Exact Solitary wave and periodic wave solutions of a class of higher-order nonlinear wave equations. (submitted)

Zhang, LJ, Khalique, CM: Exact solitary wave and periodic wave solutions of the Kaup-Kuperschmidt equation. J. Appl. Anal. Comput. 5(3), 485-495 (2015)

Guckenheimer, J, Holmes, P: Dynamical Systems and Bifurcations of Vector Fields. Springer, New York (1983)

Chow, SN, Hale, JK: Method of Bifurcation Theory. Springer, New York (1981)

Li, JB: Singular Traveling Wave Equations: Bifurcations and Exact Solutions. Science Press, Beijing (2013)

Li, JB, Chen, GR: Bifurcations of traveling wave solutions for four classes of nonlinear wave equations. Int. J. Bifurc. Chaos 15(12), 3973-3998 (2005)

Li, JB, Qiao, ZJ: Explicit solutions of the Kaup-Kuperschmidt equation through the dynamical system approach. J. Appl. Anal. Comput. 1(2), 243-250 (2011)

Zhang, LJ, Chen, LQ, Huo, XW: The effects of horizontal singular straight line in a generalized nonlinear Klein-Gordon model equation. Nonlinear Dyn. 72(4), 789-801 (2013)

Rui, WG: Different kinds of exact solutions with two-loop character of the two-component short pulse equations of the first kind. Commun. Nonlinear Sci. Numer. Simul. 18, 2667-2678 (2013)

Chen, AY, Wen, SQ, Huang, WT: Existence and orbital stability of periodic wave solutions for the nonlinear Schrödinger equation. J. Appl. Anal. Comput. 2(2), 137-148 (2012)