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Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation. (English) Zbl 1027.35119
Summary: The focusing and the defocusing branches of nonlinear Klein-Gordon-type equation $KG(n,n)$ are considered. A framework is implemented to show that the first model exhibits compactons: solitons that do not have exponential tails, whereas the second model demonstrates solitary patterns solutions. The two variants of $KG(n,n)$ equation are examined in one and higher dimensions. General formulas will be developed to present a fairly complete understanding of the solutions of compact and noncompact structures.

##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35Q51 Soliton-like equations 37K40 Soliton theory, asymptotic behavior of solutions
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##### References:
 [1] Kivshar, Y.: Compactons in discrete lattices. Nonlinear coherent struct. Phys. biol. 329, 255-258 (1994) [2] Dinda, P. T.; Remoissenet, M.: Breather compactons in nonlinear Klein--Gordon systems. Phys. rev. E 60, No. 3, 6218-6221 (1999) [3] Rosenau, P.; Hyman, J. M.: Compactons: solitons with finite wavelengths. Phys. rev. Lett. 70, No. 5, 564-567 (1993) · Zbl 0952.35502 [4] Rosenau, P.: Nonlinear dispersion and compact structures. Phys. rev. Lett. 73, No. 13, 1737-1741 (1994) · Zbl 0953.35501 [5] Rosenau, P.: On nonanalytic solitary waves formed by a nonlinear dispersion. Phys. lett. A 230, No. 5/6, 305-318 (1997) · Zbl 1052.35511 [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] Dusuel, S.; Michaux, P.; Remoissenet, M.: From kinks to compactonlike kinks. Phys. rev. E 57, No. 2, 2320-2326 (1998) [9] Ludu, A.; Stoitcheva, G.; Draayer, J. P.: Similarity analysis of nonlinear equations and bases of finite wavelength solitons. Int. J. Mod. phys. E 9, No. 3, 263-278 (2000) [10] Ludu, A.; Draayer, J. P.: Patterns on liquid surfaces: cnoidal waves compactons and scaling. Physica D 123, 82-91 (1998) · Zbl 0952.76008 [11] Ismail, M. S.; Taha, T.: A numerical study of compactons. Math. comput. Simulat. 47, 519-530 (1998) · Zbl 0932.65096 [12] Wazwaz, A. M.: New solitary-wave special solutions with compact support for the nonlinear dispersive $K(m,n)$ equations. Chaos solitons & fractals appl. 13, No. 2, 321-330 (2002) · Zbl 1028.35131 [13] Wazwaz, A. M.: Exact specific solutions with solitary patterns for the nonlinear dispersive $K(m,n)$ equations. Chaos, solitons & fractals 13, No. 1, 161-170 (2001) [14] Wazwaz, A. M.: General compactons solutions for the focusing branch of the nonlinear dispersive $K(n,n)$ equations in higher dimensional spaces. Appl. math. Comput. 133, 213-227 (2002) · Zbl 1027.35117 [15] 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. Comput. 133, 229-244 (2002) · Zbl 1027.35118 [16] 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 [17] Wazwaz, A. M.: A computational approach to soliton solutions of the Kadomtsev--petviashili equation. Appl. math. Comput. 123, No. 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 & fractals 12, No. 8, 1549-1556 (2001) · Zbl 1022.35051 [19] Wazwaz, A. M.: A first course in integral equations. (1997) · Zbl 0924.45001 [20] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · 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