@Hullzie16 

Thank you for your kind response.

The function  "u" is defined as "u=u(x,y,t) " , and "u_x" denotes the derivative of u with respect to ,  and "u_y" denotes the derivative of u with respect to y.

The operators are

L=u² .∂²/∂x² + ∂/∂y

T= 4u³ . ∂³/∂x³ + [6u².u_x - 6u² . int(u_y/u²,dx)] ∂/∂x - ∂/∂t.

For your second equation, once the operator T operates on L, and then the second operator L operates on T. These operators do not operate on another function; they operate on each other.

Thank you for taking the time to answer my question.