In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal...In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal waves in deep water and the long surface gravity waves of small amplitude propagating uni-directionally.The method can be regarded as an extension of the(G/G)-expansion method.The ansatz of this extension method to obtain the solution is based on homogeneous balance between the highest order dispersion terms and nonlinearity which is similar to the(G/G)method whereas the auxiliary linear ordinary differential equation(LODE)and polynomial solution differs.We applied this method to find explicit form solutions to the Burger’s and Benjamin-Bona-Mahony(BBM)equations to examine the effectiveness of the method and tested through mathematical computational software Maple.Some new exact travelling wave solutions in more general form of these two nonlinear equations are derived by this extended method.The method introduced here appears to be easier and faster comparatively by means of symbolic computation system.展开更多
This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations(NLEEs)through the application of the(G/G,1/G)-expansion method.This method is allied to the wid...This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations(NLEEs)through the application of the(G/G,1/G)-expansion method.This method is allied to the widely used(G/G)-method initiated by Wang et al.and can be considered as an extension of the(G/G)-expansion method.For effectiveness,the method is applied to the family of KdV type equations.Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method.Moreover,in the obtained wider set of solutions,if we set special values of the parameters,some previously known solutions are revived.The approach of this method is simple and elegantly standard.Having been computerized it is also powerful,reliable and effective.展开更多
文摘In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal waves in deep water and the long surface gravity waves of small amplitude propagating uni-directionally.The method can be regarded as an extension of the(G/G)-expansion method.The ansatz of this extension method to obtain the solution is based on homogeneous balance between the highest order dispersion terms and nonlinearity which is similar to the(G/G)method whereas the auxiliary linear ordinary differential equation(LODE)and polynomial solution differs.We applied this method to find explicit form solutions to the Burger’s and Benjamin-Bona-Mahony(BBM)equations to examine the effectiveness of the method and tested through mathematical computational software Maple.Some new exact travelling wave solutions in more general form of these two nonlinear equations are derived by this extended method.The method introduced here appears to be easier and faster comparatively by means of symbolic computation system.
文摘This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations(NLEEs)through the application of the(G/G,1/G)-expansion method.This method is allied to the widely used(G/G)-method initiated by Wang et al.and can be considered as an extension of the(G/G)-expansion method.For effectiveness,the method is applied to the family of KdV type equations.Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method.Moreover,in the obtained wider set of solutions,if we set special values of the parameters,some previously known solutions are revived.The approach of this method is simple and elegantly standard.Having been computerized it is also powerful,reliable and effective.
