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New solitary solutions with compact support for Boussinesq-like $B(2n, 2n)$ equations with fully nonlinear dispersion. (English) Zbl 1139.35091
Summary: The Boussinesq-like equations $B(2n, 2n)$ with fully nonlinear dispersion: $u_{tt} + (u^{2n})_{xx} + (u^{2n})_{xxxx} = 0$, which exhibit compactons, i.e., solitons with compact support, are studied. New exact solitary solutions with compact support are found. The special case $B$(2, 2) is chosen to illustrate the concrete scheme of the decomposition method in $B(2n, 2n)$ equations. General formulas for the solutions of $B(2n, 2n)$ equations are established.

35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
35C10Series solutions of PDE
35A25Other special methods (PDE)
Full Text: DOI
[1] 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
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[3] Yan, Z.: 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
[4] Zhu, Y.: Exact special solutions with solitary patterns for Boussinesq-like $B(m,n)$ equations with fully nonlinear dispersion. Chaos, solitons & fractals 22, 213-220 (2004) · Zbl 1062.35125
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[7] Adomian, G.: Nonlinear stochastic operator equations. (1986) · Zbl 0609.60072