# GMPDE

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### Generalized Microstructure PDE

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

**Failed to parse (syntax error): {\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]