The \((G'/ G, 1 / G)\)-expansion method and its applications to find the exact solutions of nonlinear PDEs for nanobiosciences. (English) Zbl 1407.35184
Summary: The two-variable (\(G'/ G, 1 / G\))-expansion method is employed to construct exact traveling wave solutions with parameters of nanobiosciences partial differential equation. When the parameters are replaced by special values, the solitary wave solutions and the periodic wave solutions of this equation have been obtained from the traveling waves. This method can be thought of as the generalization of well-known original \(\left(G'/ G\right)\)-expansion method proposed by M. Wang et al. It is shown that the two-variable (\(G'/ G, 1 / G\))-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics. Comparison between our results and the well-known results is given.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C07 | Traveling wave solutions |
| 35Q51 | Soliton equations |
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