The model was independently proposed by Yakov Frenkel and Tatiana Kontorova in their 1938 article On the theory of plastic deformation and twinning to describe the dynamics of a crystal lattice near a dislocation and to describe crystal twinning. In the standard linear harmonic chain any displacement of the atoms will result in waves, and the only stable configuration will be the trivial one. For the nonlinear chain of Frenkel and Kontorova, there exist stable configurations beside the trivial one. For small atomic displacements the situation resembles the linear chain; however, for large enough displacements, it is possible to create a moving single dislocation, for which an analytical solution was derived by Frenkel and Kontorova. The shape of these dislocations is defined only by the parameters of the system such as the mass and the elastic constant of the springs.