Consider the following linear wave equation. $$ u_t+cu_x-\gamma u_{xx}+\delta u_{xxx}=0 $$
If we know the following initial data, $$ u(x,0)= 3\cos^2(x)+\sin(x) $$ how to get an explicit solution?
I know that the general solution is: $$ v(x,t)=A\exp( ik[x-(c-\delta k^2)t] )\exp(-\gamma k^2t) $$
Even if I compare $u(x,0)=v(x,0)$, I can not solve it.