# zbMATH — the first resource for mathematics

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.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 35C10 Series solutions to PDEs 35A25 Other special methods applied to PDEs
##### Keywords:
nonlinear dispersion; Adomian decomposition method
Full Text:
##### References:
 [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 [2] Yan, Z., Commun theor phys (Beijing, China), 36, 385-390, (2001) [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 [5] Adomian, G., Solving frontier problems of physics:the decomposition method, (1994), Kluwer Academic Publishers Boston [6] Adomian, G., A review of the decomposition method in applied mathematics, J math anal appl, 135, 501-544, (1988) · Zbl 0671.34053 [7] Adomian, G., Nonlinear stochastic operator equations, (1986), Academic Press San Diego · Zbl 0614.35013
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.