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General compactons solutions for the focusing branch of the nonlinear dispersive \(K(n,n)\) equations in higher-dimensional spaces. (English) Zbl 1027.35117
Summary: We study the focusing branch of the genuinely nonlinear dispersive \(K(n,n)\) equation that exhibits compactons: solitons with finite wavelengths. The equation is studied in one-, two- and three-dimensional spaces. General formulas for compactons solutions are developed for all positive integers \(n\), \(n<1\). We give formulas for compactons for even integers \(n\) and for compactons and anticompactons for odd integers \(n\), \(n>1\).

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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[1] Dinda, P.T.; Remoissenet, M., Breather compactons in nonlinear klein – gordon systems, Phys. rev. E, 60, 3, 6218-6221, (1999)
[2] Rosenau, P.; Hyman, J.M., Compactons: solitons with finite wavelengths, Phys. rev. lett., 70, 5, 564-567, (1993) · Zbl 0952.35502
[3] Rosenau, P., Nonlinear dispersion and compact structures, Phys. rev. lett., 73, 13, 1737-1741, (1994) · Zbl 0953.35501
[4] Rosenau, P., On nonanalytic solitary waves formed by a nonlinear dispersion, Phys. lett. A, 230, 5/6, 305-318, (1997) · Zbl 1052.35511
[5] Rosenau, P., On a class of nonlinear dispersive – dissipative interactions, Physica D, 230, 5/6, 535-546, (1998) · Zbl 0938.35172
[6] Olver, P.J.; Rosenau, P., Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. rev. E, 53, 2, 1900-1906, (1996)
[7] Dusuel, S.; Michaux, P.; Remoissenet, M., From kinks to compacton-like kinks, Phys. rev. E, 57, 2, 2320-2326, (1998)
[8] Ludu, A.; Draayer, J.P., Patterns on liquid surfaces: cnoidal waves, compactons and scaling, Physica D, 123, 82-91, (1998) · Zbl 0952.76008
[9] Ismail, M.S.; Taha, T., A numerical study of compactons, Math. comput. simul., 47, 519-530, (1998) · Zbl 0932.65096
[10] Wazwaz, A.M., New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations, Chaos, solitons fractals, appl., 13, 321-330, (2002) · Zbl 1028.35131
[11] Wazwaz, A.M., Exact specific solutions with solitary patterns for the nonlinear dispersive K(m,n) equations, Chaos, solitons fractals, appl., 13, 161-170, (2002) · Zbl 1027.35115
[12] Wazwaz, A.M., A computational approach to soliton solutions of the kadomtsev – petviashili equation, Appl. math. comput., 123, 205-217, (2001) · Zbl 1024.65098
[13] Wazwaz, A.M., Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method, Chaos, solitons fractals, appl., 12, 1549-1556, (2001) · Zbl 1022.35051
[14] Wazwaz, A.M., A first course in integral equations, (1997), World Scientific Singapore
[15] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston, MA · Zbl 0802.65122
[16] Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. appl., 135, 501-544, (1998) · Zbl 0671.34053
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