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An analytic study of compactons structures in a class of nonlinear dispersive equations. (English) Zbl 1021.35092
Summary: We present an analytic study of the compactons structures in a class of nonlinear dispersive equations. The compactons: new form of solitary waves with compact support and width independent of amplitude, are formally constructed. We further establish solitary patterns solutions for the defocusing branches of these dispersive models.

35Q51Soliton-like equations
37K40Soliton theory, asymptotic behavior of solutions
Full Text: DOI
[1] Dey, B.; Eleftheriou, M.; Flach, S.; Tsironis, G.: Shape profile of compactlike discrete breathers in nonlinear dispersive lattice systems. Phys. rev. E 65, 17601-17604 (2001)
[2] Rosenau, P.; Hyman, J. M.: Compactons: solitons with finite wavelengths. Phys. rev. Lett. 70, No. 5, 564-567 (1993) · Zbl 0952.35502
[3] Rosenau, P.: Nonlinear dispersion and compact structures. Phys. rev. Lett. 73, No. 13, 1737-1741 (1994) · Zbl 0953.35501
[4] Rosenau, P.: On nonanalytic solitary waves formed by a nonlinear dispersion. Phys. lett. A 230, No. 5--6, 305-318 (1997) · Zbl 1052.35511
[5] Rosenau, P.: On a class of nonlinear dispersive--dissipative interactions. Physica D 230, No. 5--6, 535-546 (1998) · Zbl 0938.35172
[6] Rosenau, P.: Compact and noncompact dispersive structures. Phys. lett. A 275, No. 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, No. 2, 1900-1906 (1996)
[8] Cooper, F.; Hyman, J.; Khare, A.: Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations. Phys. rev. E 64, No. 2, 1-5 (2001)
[9] Kivshar, Y.: Compactons in discrete lattices. Nonlinear coherent struct. Phys. biol. 329, 255-258 (1994)
[10] Dinda, P. T.; Remoissenet, M.: Breather compactons in nonlinear Klein--Gordon systems. Phys. rev. E 60, No. 3, 6218-6221 (1999)
[11] Dusuel, S.; Michaux, P.; Remoissenet, M.: From kinks to compactonlike kinks. Phys. rev. E 57, No. 2, 2320-2326 (1998)
[12] Ludu, A.; Draayer, J. P.: Patterns on liquid surfaces: noidal waves, compactons and scaling. Physica D 123, 82-91 (1998) · Zbl 0952.76008
[13] Ismail, M. S.; Taha, T.: A numerical study of compactons. Math. comput. Simulat. 47, 519-530 (1998) · Zbl 0932.65096
[14] Wazwaz, A. -M.: New solitary-wave special solutions with compact support for the nonlinear dispersive $K(m,n)$ equations. Solitons fractals 13, No. 22, 321-330 (2002) · Zbl 1028.35131
[15] Wazwaz, A. -M.: Exact specific solutions with solitary patterns for the nonlinear dispersive $K(m,n)$ equations. Solitons fractals 13, No. 1, 161-170 (2001)
[16] Wazwaz, A. -M.: General compactons solutions for the focusing branch of the nonlinear dispersive $K(n,n)$ equations in higher dimensional spaces. Solitons fractals 13, No. 20, 321-330 (2002)
[17] Wazwaz, A. -M.: A study of nonlinear dispersive equations with solitary-wave solutions having compact support. Math. comput. Simulat. 56, 269-276 (2001) · Zbl 0999.65109
[18] A.-M. Wazwaz, Solutions of compact and noncompact structures for nonlinear Klein--Gordon-type equation, Appl. Math. Comput. 134 (2003) 487--500. · Zbl 1027.35119
[19] A.-M. Wazwaz, Compactons and solitary patterns structures for variants of the KdV and the KP equations, Appl. Math. Comput. 139 (2003). · Zbl 1029.35200
[20] A.-M. Wazwaz, The effect of the order of nonlinear dispersive equation on the compact and noncompact solutions, Appl. Math. Comput. 139 (2003). · Zbl 1029.35201
[21] A.-M.Wazwaz, A construction of compact and noncompact solutions for nonlinear dispersive equations of even order, Appl. Math. Comput. 135 (2003) 411--424. · Zbl 1027.35121
[22] Chertock, A.; Levy, D.: Particle methods for dispersive equations. J. comput. Phys. 171, 708-730 (2001) · Zbl 0991.65008
[23] A.-M. Wazwaz, Partial Differential Equations: Methods and Applications, A.A. Balkema Publishers, Lisse, The Netherlands, 2002.
[24] Wazwaz, A. -M.: Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Solitons fractals 12, No. 8, 1549-1556 (2001) · Zbl 1022.35051
[25] A.-M. Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, 1997. · Zbl 0924.45001
[26] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994. · Zbl 0802.65122
[27] Adomian, G.: A review of the decomposition method in applied mathematics. J. math. Anal. appl. 135, 501-544 (1998) · Zbl 0671.34053