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Applications of HTA and EHTA to YTSF equation. (English) Zbl 1159.35408
Summary: Homoclinic test approach (HTA) and extended homoclinic test approach (EHTA) are proposed to seek solitary-wave solution of high dimensional nonlinear wave system. Exact periodic solitary-wave, periodic soliton, cross solitary-wave and doubly periodic wave solutions for YTSF equation are obtained using HTA and EHTA, respectively.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35B10 Periodic solutions to PDEs
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[1] M. Tajiri, T. Arai, Periodic soliton solutions to the Davey-Stewartson equation, in: Proceedings of the Institute of Math. of NAS of Ukraine, vol. 30, 2000, pp. 210-217. · Zbl 0956.35117
[2] Yomba, E., Construction of new soliton-like solutions for the (2+1)dimensional kadomtsev – petviashvili equation, Chaos solitons fract, 22, 321-325, (2004) · Zbl 1063.35141
[3] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering, (1991), Cambridge University Press New York · Zbl 0762.35001
[4] Konopechenko, B., Solitons in multidimensions, inverse spectral transform method, (1993), World Scientific Press · Zbl 0836.35002
[5] Dai, Z.; Li, S.; Li, D.; Zhu, A., Periodic bifurcation and soliton deflexion for kadomtsev – petviashvili equation, Chin. phys. lett., 24, 1429-1433, (2007)
[6] Yu, S.J.; Toda, K.; Sasa, N.; 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, 3337-3347, (1998) · Zbl 0927.35102
[7] Schff, J., Painleve transendent, Their asymptotics and physical applications, (1992), Plenum New York
[8] Yan, Z., New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation, Phys. lett. A, 318, 78-83, (2003) · Zbl 1045.35072
[9] Dai, Z.; Huang, J.; Jiang, M., Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary, Phys. lett. A, 352, 411-415, (2006) · Zbl 1187.37112
[10] Dai, Z.; Huang, J., Homoclinic tubes for the davey – stewartson II equation with periodic boundary conditions, J. chin. phys., 43, 349-360, (2005)
[11] Dai, Z.; Li, Z.; Liu, Z.; Li, D., Exact homoclinic wave and soliton solutions for the 2D ginzburg – landau equation, Phys. lett. A, 372, 3010-3014, (2008) · Zbl 1220.35168
[12] Dai, Z.; Jiang, M.; Dai, Q.; Li, S., Homoclinic bifurcation for Boussinesq equation with even constraint, Chin. phys. lett., 23, 1065-1067, (2006)
[13] Dai, Z.; Huang, J.; Jiang, M.; Wang, S., Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint, Chaos solitons fract., 26, 1189-1194, (2005) · Zbl 1070.35029
[14] Dai, Z.; Li, S.; Dai, Q.; Huang, J., Singular periodic soliton solutions and resonance for the kadomtsev – petviashvili equation, Chaos solitons fract., 34, 1148-1153, (2007) · Zbl 1142.35563
[15] Dai, Z.; Liu, Z.; Li, D., Exact periodic solitary-wave solution for KdV equation, Chin. phys. lett., 25, 1531-1533, (2008)
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