A further improved ( G ′ G ) - expansion method and the extended tanh - method for finding exact solutions of nonlinear PDEs
نویسنده
چکیده
In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the (1 + 1) dimensional modified Kawahara equation by using the following two methods: (i) A further improved ( ′ G )expansion method, where G = G(ξ) satisfies the auxiliary ordinary differential equation [G′(ξ)]2 = aG2(ξ) + bG4(ξ) + cG6(ξ), where ξ = x − V t while a, b, c and V are constants. (ii) The well known extended tanhfunction method. We show that the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before. Key–Words: ( ′ G )expansion method, auxiliary equation, extended tanhfunction method, traveling wave solutions, modified Kawahara equation.
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