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Exact three-wave solution for higher dimensional KdV-type equation. (English) Zbl 1188.35169
Summary: A new periodic type of three-wave solutions including periodic two-solitary solution, doubly periodic solitary solution and breather type of two-solitary solution for the (1+2)-dimensional and (1+3)-dimensional KdV-type equations are obtained using Hirota’s bilinear form and generalized three-wave type of ansatz approach.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35C08Soliton solutions of PDE
35B10Periodic solutions of PDE
35A24Methods of ordinary differential equations for PDE
References:
[1]Ablowitz, M. J.; Clarkson, P. A.: Solitons, Nonlinear evolution equations and inverse scattering (1991) · Zbl 0762.35001
[2]Hirota, R.: Exact solution of the Korteweg – de-Vries equation for multiple collisions of solitons, Phys. lett. A. 27, 1192-1194 (1971) · Zbl 1168.35423 · doi:10.1103/PhysRevLett.27.1192
[3]Miurs, M. R.: Bäcklund transformation, (1978)
[4]Sawada, K.; Kotera, T.: A method for finding N-soliton solutions of the KdV equation and KdV-like equation, Prog. theor. Phys 51, 1355-1362 (1974) · Zbl 1125.35400 · doi:10.1143/PTP.51.1355
[5]Yan, C.: A simple transformation for nonlinear waves, Phys. lett. A 224, 77-784 (1996) · Zbl 1037.35504 · doi:10.1016/S0375-9601(96)00770-0
[6]Wang, M. L.: Exact solutions for a compound KdV – burger equation, Phys. lett. A 213, 279-287 (1996) · Zbl 0972.35526 · doi:10.1016/0375-9601(96)00103-X
[7]El-Wakil, S. A.; Abdou, M. A.: New exact travelling wave solutions of two nonlinear physical models, Non-linear anal 68, 235-245 (2008) · Zbl 1135.34003 · doi:10.1016/j.na.2006.10.045
[8]Boiti, M.; Leon, J.; Manna, M.; Pempinelli, F.: On the spectral transform of Korteweg – de Vries equation in two spatial dimensions, Inverse prob. 2, 271-279 (1986) · Zbl 0617.35119 · doi:10.1088/0266-5611/2/3/005
[9]Wazwaz, A. M.: Single and multiple-soliton solutions for the (2+1)-dimensional KdV equation, Appl. math. Comput. 204, 20-26 (2008) · Zbl 1160.35531 · doi:10.1016/j.amc.2008.05.126
[10]Zayad, E. M. E.; Zedan, H. A.; Gepreel, K. A.: Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equation, Int. J. Nonlinear sci. Numer. simul. 5, 221 (2004)
[11]Zhang, S.: A generalized auxiliary equation method and its application to the (2+1)-dimensional KdV equation, Appl. math. Comput. 188, 1-6 (2007) · Zbl 1114.65355 · doi:10.1016/j.amc.2006.09.068
[12]Zhang, S.: Exp-function method exactly solving a KdV equation with forcing term, Appl. math. Comput. 197, 128-134 (2008) · Zbl 1135.65388 · doi:10.1016/j.amc.2007.07.041
[13]He, J. H.; Wu, X. H.: Exp-function method for nonlinear wave equation, Chaos solitons frac. 30, 700-708 (2006) · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[14]Dai, Z. D.; Liu, Z. J.; Li, D. L.: Exact periodic solitary-wave solution for KdV equation, Chin. phys. Lett. 25, 1531-1532 (2008)
[15]Dai, Z. D.; Jiang, M. R.; Dai, Q. Y.; Li, S. L.: Homoclinic bifurcation for Boussinesq equation with even constrain, Chin. phys. Lett. 23, 1065-1067 (2006)
[16]Dai, Z. D.; Liu, J.; Li, D. L.: Applications of HTA and EHTA to YTSF equation, Appl. math. Comput. 207, 360-364 (2009) · Zbl 1159.35408 · doi:10.1016/j.amc.2008.10.042
[17]Dai, Z. D.; Liu, J.; Zeng, X. P.; Liu, Z. J.: Periodic kink-wave and kinky periodic-wave solutions for the Jimbo – Miwa equation, Phys. lett. A 372, 5984-5986 (2008) · Zbl 1223.35267 · doi:10.1016/j.physleta.2008.07.064
[18]Wang, C. J.; Dai, Z. D.; Mu, G.; Lin, S. Q.: New exact periodic solitary-wave solutions for new (2+1)-dimensional KdV equation, Commun. theor. Phys. 52, 862-864 (2009) · Zbl 1186.35193 · doi:10.1088/0253-6102/52/5/21
[19]Lou, S. Y.: Dromion-like structures in a (3+1)-dimensional KdV-type equation, J. phys. A: math. Gen., No. 29, 5989-6001 (1996) · Zbl 0903.35064 · doi:10.1088/0305-4470/29/18/027