I am looking for an analytic solution for the following two equations in the variables v(x,t)and u(x,t): ∂v/∂x= -m∂u/∂t and ∂u/∂x= -n∂v/∂t-av^5 The boundary conditions are v(0,t)=E and u(l,t)=0 The constants m,n,a,E and l are positive and non-zero. Thanks in advance. Note: This is a simplified version of my earlier (unanswered) question posted on February 13, 2019.