A nonlinear Schrodinger equation in one-dimensional bead chain is first obtained and an envelope solitary wave of the system is verified numerically in this system. The reflection and the transmission of an incident envelope solitary wave due to impurities has also been investigated. It is found that the magnitudes of both the reflection and the transmission not only depend on the characters of impurity materials, the wave number, the incident wave amplitude, but also on the impurity number. This can be used to detect the character and the number of the impurity materials in the bead chain by measuring the reflection and the transmission of an incident pulse.
The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ ＋∞.
The new coupled KdV equation proposed by Ohta and Hirota, in which the phase shift depends on the mutual positions of solitons at the initial time, is investigated in the framework of prolongation structure theory. Its Lax representation is constructed.
