Research of non-integrable systems by means of bilinear method

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We studied the discretization of differential equations to obtain the information of transformation between non-integrable differential equations and their bilinear forms. To this end, we completed the REDUCE program for finding analytic form of conserved densities of diference-difference equations. By using the program, we studied the stability of the model equation which has modified Bessel type potential, and confirm there exists nearly stable solitary wave solutions. The explicit bilinear form and the transformation of the model equation are now searching. In connection with conserved density of difference equations, we clarified the relation between the shift operator and the discrete Euler operator. Furthermore, a new approach for the study of the integrability of differential-difference systems is introduced. Each investigators of our research group achieved many accomplishment in their fields, and contributed to the progress of the present work.