# GMPDE

### Generalized Microstructure PDE

One dimensional wave propagation in microstructured solids has recently been modeled by an equation

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle v_{tt} - b v_{xx} − \frac{\mu }{2}\left( v \right)_{xx} − \delta \left(\beta v_{tt} - \gamma v_{xx} \right)_{xx} = 0 }**

It admits embedded solitons of the form when . The constants and depend on and is the wave speed after the coordinate transformation .

This equation has the property of being a reversible system, and therefore one may find the exact solution without resorting to the Inverse Scattering Transform by using properties of reversible systems to recast the equation in terms of a bilinear operator.

[Abtstract for Solitary wave families of a generalized microstructure PDE]