×

Exact three-wave solutions for the KP equation. (English) Zbl 1191.35228

Summary: A new type of three-wave solution, periodic two-solitary-wave solutions, for \((1+2)\)D Kadomtsev-Petviashvili (KP) equation is obtained using the extended three-soliton method and with the help of Maple.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35C08 Soliton solutions
35-04 Software, source code, etc. for problems pertaining to partial differential equations

Software:

Maple
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution and inverse scattering, (1991), Cambridge University Press · Zbl 0762.35001
[2] Konopechenko, B., Solitons in, multidimensions inverse spectral transform method, (1993), World Scientific · Zbl 0836.35002
[3] Kadomtsev, B.B.; Petviashvili, V.I., On the stability of solitary waves in weakly dispersive media, Soviet. phys. dokl., 15, 539-541, (1970) · Zbl 0217.25004
[4] Ukai, S., Local solutions of the kadomtsev – petviashvili equation, J. fac. sci. univ. Tokyo, sect. IA math., 36, 193-209, (1989) · Zbl 0703.35155
[5] Bakuzov, V.; Rbuiioug, H.K.; Jiang, Z.; Manakov, S.V., Complete integrability of the KP equation, Physica D, 28, 1, 235, (1987)
[6] Cheng, Y.; Li, Y.S., The constraint of the kadomtsev – petviashvili equation and its special solutions, Phys. lett. A, 157, 22-26, (1991)
[7] Isaza, P.; Mejia, J.; Stallbohm, V.J., Local solution for the kadomtsev – petviashvili equation in \(R^2\), Math. anal. appl., 196, 2, 566-587, (1995) · Zbl 0844.35107
[8] Tajiri, M.; Watanabe, Y., Periodic soliton solutions as imbricate series of rational solitons:solutions to the kadomtsev – petviashvili equation with positive dispersion, Nonlinear math. phys., 4, 3-4, 350-357, (1997) · Zbl 0949.35123
[9] Zhu, J., Multisoliton excitations for the kadomtsev – petviashvili equation and the coupled Burgers equation, Chaos soliton fract., 31, 3, 648-657, (2007) · Zbl 1139.35391
[10] Yomba, E., Construction of new soliton-like solutions for the (2+1)dimensional kadomtsev – petviashvili equation, Chaos soliton fract., 22, 2, 321-325, (2004) · Zbl 1063.35141
[11] Tagumi, Y., Soliton-like solutions to a (2+1)-dimensional generalization of the KdV equation, Phys. lett. A, 141, 116-120, (1989)
[12] Biswas, Anjan; Ranasinghe, Arjuna, 1-soliton solution of the kadomtsev – petviashvili equation with power law nonlinearity, App. math. comput., 214, 645-647, (2009) · Zbl 1172.35476
[13] Biswas, Anjan; Ranasinghe, Arjuna, 1-soliton solution of the kadomtsev – petviashvili equation with power law nonlinearity, Appl. math. comput., 214, 645-647, (2009) · Zbl 1172.35476
[14] Dai, Z.; Huang, Y.; Sun, X.; Li, D.; Hu, Z., Exact singular and non-singular solitary-wave solutions for kadomtsev – petviashvili equation with p-power of nonlinearity, Chaos soliton fract., 40, 946-951, (2009) · Zbl 1197.35221
[15] Dai, Z.; Li, S.; Dai, Q.; Huang, J., Singular periodic soliton solutions and resonance for the kadomtsev – petviashvili equation, Chaos soliton fract., 34, 4, 1148-1153, (2007) · Zbl 1142.35563
[16] Dai, Z.; Li, S.; Li, D.; Zhu, A., Periodic bifurcation and soliton deflexion for kadomtsev – petviashvili equation, Chin. phys. lett., 24, 6, 1429-1433, (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.