Does the PDE $u_{tt} = a u_{xx} + b u_{xxxx}$ have a name?

Question

I stumbled upon an interesting PDE in my work, but failed to find its name or type (if it has one).

$$u = u(x,t)$$

$$u_{tt} = a u_{xx} + b u_{xxxx}$$

Here the subscripts denote partial derivatives, while $a$ and $b$ are some real constants. Thanks for your help!

Answer 1

If $a>0$ and $b<0$, then this equation is also known as the stiff string wave equation, which models the transverse motion of a non-ideal string by accounting for bending stiffness (see e.g. link1, link2, link3). It belongs to the class of linear dispersive wave equations.