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Compact and noncompact solutions for the BBM\((n,n)\) equation. (English) Zbl 1067.35022

Summary: Special type of the Benjamin-Bona-Mahony equation BBM\((n,n)\) is studied for compact and noncompact solutions. The sine-cosine method features a variety of exact travelling wave solutions for this equation. The obtained solutions include compactons, solitons, solitary patterns, and periodic solutions.

MSC:

35C05 Solutions to PDEs in closed form
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35B10 Periodic solutions to PDEs