Application of Soliton Theory to Engineering

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The purpose of this research is to contribute to the development of engineering by applying the idea of soliton theory to the field. The following results are obtained through the research.(1)Numerical Analysis : Relationship of discrete soliton equations with LR-and QR methods is investigated. It is shown that the symmetry properties of soliton equations are extracted from the LR method. Relationships with accelaration method and extrapolation formula are also studied and a new accelaration scheme is proposed.(2)Engineering Mathematics : It is pointed out that the tau function in the soliton theory plays important roles also in the linear system theory, Karmarker method and information geometry. Moreover, it is revealed that the solutions of discrete Painleve equations are closely related to those of the Toda equation.(3)Information Engineering : The structure of soliton cellular automata is clarified by employing a concept of "ultra-discrete limit". New insight on storage and compression of solitons in the discrete electrical circuit is also obtained.(4)Structural Analysis : The possibility of existence of string solution for optical exiton is shown by applying the integrable property in the quantum spin system.