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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.

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
Full Text: DOI
[1] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering, (1991), Cambridge University Press Cambridge · Zbl 0762.35001
[2] Matsuno, Y., Bilinear transformation method, (1984), Academic Press London · Zbl 0552.35001
[3] Matveev, V.B.; Salle, M.A., Darboux transformations and solitons, (1991), 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)
[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)
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