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Exact special solutions with solitary patterns for Boussinesq-like $B(m,n)$ equations with fully nonlinear dispersion. (English) Zbl 1062.35125
Summary: The Boussinesq-like equations with fully nonlinear dispersion ($B(m,n)$ equations), $$u_{tt}+(u^{m})_{xx}-(u^{n})_{xxxx}=0$$ which exhibit solutions with solitary patterns, are studied. New exact solitary solutions of the equations are found. The two special cases, $B(2,2)$ and $B(3,3)$, are chosen to illustrate the concrete scheme of the decomposition method in $B(m,n)$ equations. The nonlinear equations $B(m,n)$ are addressed for two different cases, namely when $m=n$ being odd and even integers. General formulas for the solutions of $B(m,n)$ equations are established.

35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
37K40Soliton theory, asymptotic behavior of solutions
Full Text: DOI
[1] Rosenau, P.; Hyman, J. M.: Compactons: solitons with finite wavelengths. Phys. rev. Lett. 70, No. 5, 564-567 (1993) · Zbl 0952.35502
[2] Wazwaz, A. M.: Exact special solutions with solitary patterns for the nonlinear dispersive $K(m,n)$ equations. Chaos, solitons & fractals 13, 161-170 (2002) · Zbl 1027.35115
[3] Wazwaz, A. M.: New solitary-wave special solutions with compact support for the nonlinear dispersive $K(m,n)$ equations. Chaos, solitons & fractals 13, 321-330 (2002) · Zbl 1028.35131
[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.: On a class of nonlinear dispersive--dissipative interactions. Phys. D 230, No. 5/6, 535-546 (1998) · Zbl 0938.35172
[7] Wazwaz, A. M.: Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Chaos, solitons & fractals 12, 1549-1556 (2001) · Zbl 1022.35051
[8] Yan, Z. Y.: Commun. theor. Phys. (Beijing, China). 36, 385-390 (2001)
[9] Yan, Z. Y.: New families of solitons with compact support for Boussinesq-like $B(m,n)$ equations with fully nonlinear dispersion. Chaos, solitons & fractals 14, 1151-1158 (2002) · Zbl 1038.35082
[10] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[11] Adomian, G.: A review of the decomposition method in applied mathematics. J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053
[12] Adomian, G.: Nonlinear stochastic operator equations. (1986) · Zbl 0609.60072