zbMATH — the first resource for mathematics

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 \(n\), \(n>1\).

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Full Text: DOI
[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
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.