Some exact explicit solutions and conservation laws of Chaffee-Infante equation by Lie symmetry analysis

In this work, the tanh method is employed to compute some traveling wave patterns of the nonlinear third-order (2+1) dimensional Chaffee-Infante (CI) equation. The tanh technique is successfully used to get the traveling wave solutions of a considered model in the form of some hyperbolic functions. The Lie symmetry technique is used to analyze the Chaffee-Infante (CI) equation and compute the Infinitesimal generators under the invariance criteria of Lie groups. Then we construct the commutator table, adjoint representation table, and we have represented symmetry groups for each Infinitesimal generator. The optimal system and similarity reduction method is used to obtain some analytical solutions of the considered model. With the help of the similarity reduction method, we have converted the nonlinear partial differential equation into nonlinear ordinary differential equations (ODEs). Moreover, we have shown graphically obtained wave solutions by using the different values of involving parameters. Conserved quantities of nonlinear CI equation are obtained by the multiplier approach.

Automated summary

In this work, the tanh method is employed to compute traveling wave patterns of the nonlinear Chaffee-Infante (CI) equation, while the Lie symmetry technique is used to analyze and compute Infinitesimal generators. The similarity reduction method is then used to convert the nonlinear partial differential equation into ordinary differential equations with numerical solutions obtained.