Abstract
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 originalG′/G-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.
Highlights
In recent years, investigations of exact solutions to nonlinear partial differential equations (PDEs) play an important role in the study of nonlinear physical phenomena
The key idea of the one-variable (G/G)-expansion method is that the exact solutions of nonlinear PDEs can be expressed by a polynomial in one variable (G/G) in which
The key idea of the two variable (G/G, 1/G)expansion method is that the exact traveling wave solutions of nonlinear PDEs can be expressed by a polynomial in two variables (G/G) and (1/G) in which G = G(ξ) satisfies the second-order linear ODE G(ξ) + λG(ξ) = μ, where λ and μ are constants
Summary
Investigations of exact solutions to nonlinear partial differential equations (PDEs) play an important role in the study of nonlinear physical phenomena. The key idea of the two variable (G/G, 1/G)expansion method is that the exact traveling wave solutions of nonlinear PDEs can be expressed by a polynomial in two variables (G/G) and (1/G) in which G = G(ξ) satisfies the second-order linear ODE G(ξ) + λG(ξ) = μ, where λ and μ are constants. The degree of this polynomial can be determined by considering the homogeneous balance between the highest order derivatives and the nonlinear terms appearing in the given nonlinear PDEs. The degree of this polynomial can be determined by considering the homogeneous balance between the highest order derivatives and the nonlinear terms appearing in the given nonlinear PDEs The coefficients of this polynomial can be obtained by solving a set of algebraic equations resulting from the process of using this method.
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