We analytically study soliton excitations in a diatomic chain with different masses and alternating force constants between the nearest neighbors by the means of multiple scales plus quasi discrete approximation method.

Derivations of shallow water wave equations and suspended sediment diffusion equations by method of multiple scales;

By virtue of the method of multiple scales, we have investigated the behavior of waves in a one-dimensional nonlinear monoatomic chain under damping and found that the amplitude of the lattice waves decreases and the group velocity becomes slow under the action of damping of an order of O(ε).

A class of two_degree_of_freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Ω is proved by the use of the method of multiple scales.

The nonlinear vibration problem of a viscoelastic rectangular plate on a viscoelastic foundation is studied by the multiple scales method.

Combining the stretched coordinate method with the multiple scales method,we constructed the uniformly valid expansion for the singular perturbation problems of first order ordinary differential equations.

Starting from Navier Stokes equation and equation of conservation of mass,multiple scale method from perturbation theory is drawn into the study of hydrodynamics in line with the characteristics of tidal current,wave,turbulence and other temporal and spatial sacles.