Research Article

Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (𝐺/𝐺)-Expansion Method

Table 1


Zayed and Gepreel [57] solutionsOur solutions

(i) If 𝑐 1 0 , 𝑐 2 = 0 , 𝜆 > 0 and 𝜇 = 0 , Equation (3.31) becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) ( c o t h ( 𝜆 / 2 ) 𝜉 2 ) .(i) If 𝜆 > 0 , 𝜇 = 0 and 𝜂 = 𝜉 , solution 𝑣 1 becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) ( c o t h ( 𝜆 / 2 ) 𝜉 2 ) .
(ii) If 𝑐 1 = 0 , 𝑐 2 0 , 𝜆 > 0 and 𝜇 = 0 , Equation (3.31) becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) ( t a n h ( 𝜆 / 2 ) 𝜉 2 ) .(ii) If 𝜆 > 0 , 𝜇 = 0 and 𝜂 = 𝜉 , solution 𝑣 3 becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) ( t a n h ( 𝜆 / 2 ) 𝜉 2 ) .
(iii) If 𝑐 1 = 0 , 𝑐 2 0 , 𝜆 = 0 and 𝜇 is positive Equation (3.32) becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) c o t ( 𝜇 𝜉 ) .(iii) If 𝜆 = 0 , 𝜇 is positive and 𝜂 = 𝜉 , solution 𝑣 7 becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) c o t ( 𝜇 𝜉 ) .
(iv) If 𝑐 1 0 , 𝑐 2 = 0 , 𝜆 = 0 and 𝜇 is positive Equation (3.32) becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) t a n ( 𝜇 𝜉 ) .(iv) If 𝜆 = 0 , 𝜇 is positive and 𝜂 = 𝜉 , solution 𝑣 9 becomes: 𝑢 ( 𝜉 ) = ± ( 𝛽 / 𝛾 ) t a n ( 𝜇 𝜉 ) .