Special Session 69: Lie Symmetries, Conservation laws and other approaches in solving nonlinear differential equations
Contents
We consider the system of generalized Drinfeld--Sokolov equations which models one-dimensional nonlinear wave processes in two-component media
$$\begin{array}{r}
u_t+\alpha_1uu_x+\beta_1u_{xxx}+\gamma(v^{\delta})_x=0,\\
v_t+\alpha_2uv_x+\beta_2v_{xxx}=0.\end{array}$$
We obtain the Lie group classification depending on the parameters. We derive the reduction to systems of ordinary differential equations from the optimal system of subalgebras. We present some particular solutions.