The formula of solution to a nonlinear ODE with an undetermined coefficient and a positive integer power term of dependent variable have been obtained by the transformation of dependent variable and $(\frac{{G'}}{G})$-expansion method. The travelling wave reduction ODEs (perhaps, after integration and identical deformation) of a class of nonlinear evolution equations with a dissipative term and a positive integer power term of dependent variable that includes GKdV-Burgers equation, GKP-Burgers equation, GZK-Burgers equation, GBoussinesq equation and GKlein-Gordon equation, are all attributed to the same type of ODEs as the nonlinear ODE considered. The kink type of travelling wave solutions for these nonlinear evolution equations are obtained in terms of the formula of solution to the nonlinear ODE considered.
Citation: Lingxiao Li, Jinliang Zhang, Mingliang Wang. The travelling wave solutions of nonlinear evolution equations with both a dissipative term and a positive integer power term[J]. AIMS Mathematics, 2022, 7(8): 15029-15040. doi: 10.3934/math.2022823
The formula of solution to a nonlinear ODE with an undetermined coefficient and a positive integer power term of dependent variable have been obtained by the transformation of dependent variable and $(\frac{{G'}}{G})$-expansion method. The travelling wave reduction ODEs (perhaps, after integration and identical deformation) of a class of nonlinear evolution equations with a dissipative term and a positive integer power term of dependent variable that includes GKdV-Burgers equation, GKP-Burgers equation, GZK-Burgers equation, GBoussinesq equation and GKlein-Gordon equation, are all attributed to the same type of ODEs as the nonlinear ODE considered. The kink type of travelling wave solutions for these nonlinear evolution equations are obtained in terms of the formula of solution to the nonlinear ODE considered.
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Lingxiao Li, Jinliang Zhang, Mingliang Wang. The travelling wave solutions of nonlinear evolution equations with both a dissipative term and a positive integer power term[J]. AIMS Mathematics, 2022, 7(8): 15029-15040. doi: 10.3934/math.2022823
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