Tailing wavetrain generation in precursor soliton generation in single-layer flow

A theory of tailing wavetrain generation in the precursor soliton generatio n in single-layer flow is presented in terms of Whitham's a averaged method in the present paper. The group characters of the tailing wavetrain genera tion are represented by the evolution equations of roots of a cubic algebra ic equation resulting from the fKdV equation in the single-layer flow witho ut source term. Based on the evolution equations, the group velocity of the tailing wavetrain is found theoretically, furthermore a theoretical soluti on of the tailing wavetrain generation is found in terms of the evolution e quations. To examine the theoretical results, a numerical calculation of fK dV equation in single-layer flow is carried out in the laboratory frame, at the same time a comparison is also done. The comparison between theoretica l and numerical results shows they are in good agreement.