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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.

##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35C05 Solutions of PDE in closed form 37K40 Soliton theory, asymptotic behavior of solutions
##### Keywords:
exact solitary solutions; decomposition method
Full Text:
##### References:
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