Abstract: Employing the coherent state ansatz and the time-dependent variational principle, we obtain a partial differential equation of motion from Hamiltonian in inharmonic molecuIar crystals. By using the method of multiple scales. we reduce this equation into the envelope function and find that the amplitude function satisfied a nonlinear Schrodinger equation. Introducing the inverse scattering transformation, we gain the single-, twry and N- soliton solutions. The energy and the spatial configurations of the system are given. We also acquire the periodic wave solution and analyze its stability.