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The homogeneous balance method and its application to the Benjamin-Bona-Mahoney (BBM) equation. (English) Zbl 1202.35209

Summary: We make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the Benjamin-Bona-Mahoney (BBM) equation. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35C08 Soliton solutions
35A24 Methods of ordinary differential equations applied to PDEs
35-04 Software, source code, etc. for problems pertaining to partial differential equations
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