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A computational approach to soliton solutions of the Kadomtsev-Petviashvili equation. (English) Zbl 1024.65098
Summary: We present a computational approach to develop soliton solutions of the nonlinear Kadomtsev-Petviashvili equation. Our approach rests mainly on the Adomian decomposition method to include few components of the decomposition series. The proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type. Numerical examples are tested to illustrate the proposed scheme.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K90 Abstract parabolic equations
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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[1] Debnath, L., Nonlinear partial differential equations for scientists and engineers, (1998), Birkhauser Berlin
[2] Bullogh, P.K.; Caudrey, P.J., Solitons, (1980), Springer Berlin
[3] Hirota, R., Direct methods in soliton theory, () · Zbl 0124.21603
[4] Freeman, N.C., Soliton solutions of non-linear evolution equations, IMA J. appl. math., 32, 125-145, (1984) · Zbl 0542.35079
[5] Freeman, N.C., Soliton interactions in two dimensions, Adv. appl. mech., 20, 1-37, (1980) · Zbl 0477.35077
[6] Kadomtsev, B.B.; Petviashvili, V.I., On the stability of solitary waves in weakly dispersive media, Sov. phys. dokl., 15, 539-541, (1970) · Zbl 0217.25004
[7] Bratsos, A.G.; Twizell, E.H., An explicit finite difference scheme for the solution of kadomtsev – petviashvili, Int. J. comput. math., 68, 175-187, (1998) · Zbl 0904.65094
[8] Grünbaum, F.A., The kadomtsev – petviashvili equation: an alternative approach to the rank two solutions of krichever and notikov, Phys. lett. A, 139, 146-150, (1989)
[9] Krichever, I.M.; Novikov, S.P., Holomorphic bundles over algebraic curves and nonlinear equations, Russ. math. surv., 35, 53-64, (1980) · Zbl 0548.35100
[10] Latham, G.A., Solutions of the KP equation associated to rank-three commuting differential operators over a singular elliptic curve, Physica D, 41, 55-66, (1990) · Zbl 0721.35078
[11] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston, MA · Zbl 0802.65122
[12] Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. appl., 135, 501-544, (1988) · Zbl 0671.34053
[13] Wazwaz, A.M., A first course in integral equations, (1997), WSPC Singapore
[14] Wazwaz, A.M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. math. comput., 111, 53-69, (2000) · Zbl 1023.65108
[15] Baker, G.A., Essentials of Padé approximants, (1975), Academic Press London
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