# zbMATH — the first resource for mathematics

A construction of compact and noncompact solutions for nonlinear dispersive equations of even order. (English) Zbl 1027.35121
Summary: A construction of compact and noncompact solutions for nonlinear dispersive partial differential equations of even order is considered. Two model equations of even orders $$k\geq 4$$ are adopted to carry out this study. The analysis reveals the presence of distinct roots of different indices that play a significant role in the solutions.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
##### Keywords:
compactons; solitons; $$K(n,n)$$ equation; cusps
Full Text:
##### References:
 [1] Dinda, P.T.; Remoissenet, M., Breather compactons in nonlinear klein – gordon systems, Phys. rev. E, 60, 3, 6218-6221, (1999) [2] Kivshar, Y., Compactons in discrete lattices, Nonlinear coherent struct. phys. biol., 329, 255-258, (1994) [3] Rosenau, P.; Hyman, J.M., Compactons: solitons with finite wavelengths, Phys. rev. lett., 70, 5, 564-567, (1993) · Zbl 0952.35502 [4] Rosenau, P., Nonlinear dispersion and compact structures, Phys. rev. lett., 73, 13, 1737-1741, (1994) · Zbl 0953.35501 [5] Rosenau, P., On nonanalytic solitary waves formed by a nonlinear dispersion, Phys. lett. A, 230, 5/6, 305-318, (1997) · Zbl 1052.35511 [6] Rosenau, P., Compact and noncompact dispersive structures, Phys. lett. A, 275, 3, 193-203, (2000) · Zbl 1115.35365 [7] 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) [8] Dusuel, S.; Michaux, P.; Remoissenet, M., From kinks to compactonlike kinks, Phys. rev. E, 57, 2, 2320-2326, (1998) [9] Ludu, A.; Draayer, J.P., Patterns on liquid surfaces:cnoidal waves, compactons and scaling, Physica D, 123, 82-91, (1998) · Zbl 0952.76008 [10] Ismail, M.S.; Taha, T., A numerical study of compactons, Math. comput. simulation, 47, 519-530, (1998) · Zbl 0932.65096 [11] Wazwaz, A.M., New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations, Chaos, solitons and fractals, 13, 2, 161-170, (2001) · Zbl 1027.35115 [12] Wazwaz, A.M., Exact specific solutions with solitary patterns for the nonlinear dispersive K(m,n) equations, Chaos, solitons and fractals, 13, 1, 161-170, (2001) · Zbl 1027.35115 [13] Wazwaz, A.M., General compactons solutions for the focusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces, Appl. math. and comput., 133, 213-227, (2002) · Zbl 1027.35117 [14] Wazwaz, A.M., General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces, Appl. math. and comput., 133, 229-244, (2002) · Zbl 1027.35118 [15] Wazwaz, A.M., A study of nonlinear dispersive equations with solitary-wave solutions having compact support, Math. comput. simulation, 56, 269-276, (2001) · Zbl 0999.65109 [16] A.M. Wazwaz, The effect of the order of nonlinear dispersive equation on the compact and noncompact solutions, Appl. Math. Comput., to appear · Zbl 1029.35201 [17] Wazwaz, A.M., A computational approach to soliton solutions of the kadomtsev – petviashili equation, Appl. math. comput., 123, 2, 205-217, (2001) · Zbl 1024.65098 [18] Wazwaz, A.M., Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method, Chaos, solitons and fractals, 12, 8, 1549-1556, (2001) · Zbl 1022.35051 [19] Wazwaz, A.M., A first course in integral equations, (1997), World Scientific Singapore [20] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston, MA · Zbl 0802.65122 [21] 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.