Wave Propagation in Nonlinear Lattice. I

A nonlinear partial differential equation which describes the wave propagation in a one-dimensional nonlinear lattice is presented and studied by various analytical methods. It is shown that the equation has periodic progressive wave, and one and two soliton solutions. It is also shown that the equation has an infinite number of conservation laws and has Bäcklund transformation. Furthermore, the application of Hirota's method to the equation is discussed.