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Unified Riccati equation expansion method and its application to two new classes of Benjamin–Bona–Mahony equations

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Abstract

The Bäcklund transformations and the superposition formulas of the Riccati equation with constant coefficients are constructed. Two fractional type solutions of the Riccati equation are obtained from its Bäcklund transformations. The equivalence relations between fractional solutions and previous known solutions are proved. A so-called unified Riccati equation expansion method for generating infinite number of exact traveling wave solutions for nonlinear evolution equations is then developed on the basis of the fractional solutions. With the method, infinitely many exact traveling wave solutions of two new classes of Benjamin–Bona–Mahony equations are presented.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 1261037 and 11361040, and by the “Ten, Hundred, Thousand” Talent Training Project of Inner Mongolia Normal University under Grant No. RCPY-2-2012-K-033.

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  1. Mathematical Science College, Inner Mongolia Normal University, Huhhot, Inner Mongolia, 010022, China

    Sirendaoreji

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Sirendaoreji Unified Riccati equation expansion method and its application to two new classes of Benjamin–Bona–Mahony equations. Nonlinear Dyn 89, 333–344 (2017). https://doi.org/10.1007/s11071-017-3457-6

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  • DOI: https://doi.org/10.1007/s11071-017-3457-6

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