| Project/Area Number |
11640121
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University |
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Principal Investigator |
ITO Masaaki Faculty of Engineering, Hiroshima University, Associate Professor, 工学部, 助教授 (10116535)
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| Co-Investigator(Kenkyū-buntansha) |
UCHIYAMA Satoki Faculty of Engineering, Hiroshima University, Research Associate, 工学部, 助手 (20304404)
OHTA Yasuhiro Faculty of Engineering, Hiroshima University, Research Associate, 工学部, 助手 (10213745)
SHIBA Masakazu Faculty of Engineering, Hiroshima University, Professor, 工学部, 教授 (70025469)
WATANABE Yoshihide Faculty of Engineering, Doshisya University, Professor, 工学部, 教授 (50127742)
SATO Manabu Faculty of Health Sciences, Hiroshima Prefectural College of Health Science, Professor, 保健福祉学部, 教授 (90178773)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Bilinear method / Non-integrable systems / Soliton / Modified Bessel function / Computer Algebra |
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| Research Abstract |
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.
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