中文摘要：

According to the basic idea of classical Yin-Yang complementarity and modern dual-complementarity,in a simple and unified new way proposed by Luo,the unconventional Gurtin-type variational prinicples for finite deformation elastodynamics can be established systemati-cally.In this paper,an important integral relation in terms of convolution is given,which canbe considered as the expression of the generalized principle of virtual work for finite deformationdynamics.Based on this relation,it is possible not only to obtain the principle of virtual work forfinite deformation dynamics,but also to derive systematically the complementary functionals forfive-field,three-field,two-field and one-field unconventional Gurtin-type variational principles bythe generalized Legendre transformations given in this paper.Furthermore,with this approach,the intrinsic relationship among various principles can be clearly explained.

英文摘要：

A theory of tailing wavetrain generation for the precursor soliton generation in two-layer flow is presented by using averaged KdV equations (AKdV), which are derived by the authors in terms of Whitham's method of averaging[1,2]. From the AKdV equations, group velocities of the tailing wavetrain generation are obtained by means of generating conditions of the tailing wavetrains, furthermore an analytical solution of the tailing wavetrain generation is found theoretically. A comparison between the theoretical and numerical results is carried out in the present paper, which shows that the theoretical results are in good agreement with the numerical ones, obtained from the fKdV equation in two-layer flow with the depth of unity in the rest.