The improved Riccati equation method and exact solutions to mZK equation. (English) Zbl 1251.34005
Summary: We use the improved Riccati equation method to construct more general exact solutions to nonlinear equations. We obtain the travelling wave solutions involving parameters, which are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. When the parameters are taken as special values, the method provides not only solitary wave solutions but also periodic waves solutions. The method appears to be easier and more convenient by means of a symbolic computation system. Of course, it is also effective to solve other nonlinear evolution equations in mathematical physics.
MSC:
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
| 35C07 | Traveling wave solutions |
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