Analytical properties of nonlinear dislocation equation

Continuum model corresponding to the generalization of both the Fermi-Pasta-Ulam and the Frenkel-Kontorova models is considered. This generalized model can be used for the description of nonlinear dislocation waves in the crystal lattice. Using the Painlevé test we analyze the integrability of this equation. We find that there exists an integrable case of the partial differential equation for nonlinear dislocations. Exact solutions of nonlinear dislocation equation are presented.