Multiple solution profiles to the higher-dimensional Kadomtsev-Petviashvilli equations via Wronskian determinant. (English) Zbl 1151.35421
Summary: Many types of new exact solutions of \((3 + 1)\)-dimensional KP equation are obtained via a unified Wronskian determinant and three linear partial differential equations, which involve many types of multiple solitary wave solutions, rational solutions, and rational-solitary wave solutions. It is shown that the collisions of the obtained multiple solitary wave solutions are elastic, which implies that \((3 + 1)\)-dimensional KP equation admits multisoliton solutions. Moreover the Wronskian formal solutions of \((n + 1)\)-dimensional KP equations are given.
Keywords:
(3+1)-dimensional KP equation; Wronskian determinant; exact solution; elastic collision; soliton solutionReferences:
| [1] | Ablowitz, M. J.; Clarkson, P. A., Solitons, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0762.35001 |
| [2] | Matsuno, Y., Bilinear transformation method (1984), Academic Press: Academic Press London · Zbl 0552.35001 |
| [3] | Matveev, V. B.; Salle, M. A., Darboux transformations and solitons (1991), Spring-Verlag: Spring-Verlag Berlin · Zbl 0744.35045 |
| [4] | Zeng, Y. B., J Phys A, 36, 5035 (2003) |
| [5] | Freeman, N. C.; Nimmo, J. J.C., Phys Lett A, 95, 1 (1983), 4 |
| [6] | Nimmo, J. J.C.; Freeman, N. C., J Phys A, 17, 1415 (1984) · Zbl 0552.35071 |
| [7] | Kuznietsov, E. A.; Turitsyn, S. K., Eksp Teor Fiz, 82, 1457 (1982) |
| [8] | Kuznietsov, E. A.; Musher, C. L., Sov Phys JETP, 64, 947 (1986) |
| [9] | Ruan, H. Y., J Phys A, 32, 2719 (1999) |
| [10] | Wang, L. Y.; Lou, S. Y., Commun Theor Phys, 33, 683 (2000) |
| [11] | Weiss, J., J Math Phys, 24, 522 (1983) |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
