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Non-integrable variants of Boussinesq equation with two solitons. (English) Zbl 1198.35242
Summary: Three variants of the Boussinesq equation, namely, the (2 + 1)-dimensional Boussinesq equation, the (3 + 1)-dimensional Boussinesq equation, and the sixth-order Boussinesq equation are studied. The Hirota bilinear method is used to construct two soliton solutions for each equation. The study highlights the fact that these equations are non-integrable and do not admit $N$-soliton solutions although these equations can be put in bilinear forms.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35C08 Soliton solutions of PDE
##### References:
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