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New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations. (English) Zbl 1196.68338
Summary: The special exact solutions of nonlinearly dispersive Boussinesq equations (called \(B(m,n)\) equations), \(u_{tt} - u_{xx} - a(u_n)_{xx}+b(u_m)_{xxxx}=0\), is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with \(m=1\). Moreover, another new compacton solution of the special case, \(B\)(2,2) equation, is also found.

MSC:
68W30 Symbolic computation and algebraic computation
35Q53 KdV equations (Korteweg-de Vries equations)
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