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Soliton and periodic solutions for higher order wave equations of KdV type (I). (English) Zbl 1070.35062
Summary: The aim of the paper is twofold. First, a new ansatz is introduced for the construction of exact solutions for higher order wave equations of KdV type (I). We show the existence of a class of discontinuous soliton solutions with infinite spikes. Second, the projective Riccati technique is implemented as an alternate approach for obtaining new exact solutions, solitary solutions, and periodic wave solutions.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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##### References:
 [1] Jeffrey, A.; Mohamad, M.N.B., Travelling wave solutions to a higher order KdV equation, Chaos, solitons & fractals, 1, 2, 187-194, (1991) · Zbl 0732.76012 [2] Li, J.; Liu, Z., Smooth and non-smooth travelling waves in a nonlinearly dispersive equation, Appl math model, 25, 41-56, (2000) · Zbl 0985.37072 [3] Li, J.; Liu, Z., Travelling wave solutions for a class of nonlinear dispersive equations, Chin. ann. math., 23B, 397-418, (2000) [4] Long, Y.; Rui, W.; He, B., Travelling solutions for a higher order wave equations of KdV type (I), Chaos, solitons & fractals, 23, 469-475, (2005) · Zbl 1069.35075 [5] Marchant, T.R., Asymptotic solitons for a third-order Korteweg-de Vries equation, Chaos, solitons & fractals, 22, 2, 261-270, (2004) · Zbl 1062.35116 [6] Mei, J.; Zhang, H.; Jiang, D., New exact solutions for a reaction-diffusion equation and a quasi-Camassa Holm equation, Appl math E-notes, 4, 85-91, (2004) · Zbl 1064.35032 [7] Tzirtztilakis, E.; Marinakis, V.; Apokis, C.; Bountis, T., Soliton-like solutions of higher order wave equations of the Korteweg-de-Vries type, J math phys, 43, 12, 6151-6161, (2002) · Zbl 1060.35127 [8] Zhang, W.; Chang, Q.; Jiang, B., Explicit exact solitary-wave solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order, Chaos, solitons & fractals, 13, 311-319, (2002) · Zbl 1028.35133 [9] Tzirtztilakis, E.; Xenos, M.; Marinakis, V.; Bountis, T., Interactions and stability of solitary waves in shallow water, Chaos, solitons & fractals, 14, 87-95, (2002) · Zbl 1068.76011 [10] Yan, Z.Y., Generalized method and its application in the higher-order nonlinear Schrödinger equation in nonlinear optical fibers, Chaos, solitons & fractals, 16, 759-766, (2003) · Zbl 1035.78006
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