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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.11 P.1466~1470

http://doi.org/10.1631/jzus.2004.1466


Generalized solutions to the Benjamin-Ono equations in sense of Colombeau


Author(s):  JIN Xiao-gang, YANG Jian-gang, LIN Jie

Affiliation(s):  Institute of Artificial Intelligence, College of Computer Science, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   xiaogangj@cise.zju.edu.cn

Key Words:  B-O equation, Algebra of generalized solution, Hilbert transform


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JIN Xiao-gang, YANG Jian-gang, LIN Jie. Generalized solutions to the Benjamin-Ono equations in sense of Colombeau[J]. Journal of Zhejiang University Science A, 2004, 5(11): 1466~1470.

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Abstract: 
This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Biaginioni, H.A., Oberguggenberger, M., 1992a. Generalized solutions to Burgrs’ equation. J. Differential Equations, 97:263-287.

[2] Biaginioni, H.A., Oberguggenberger, M., 1992b. Generalized solutions to the Korteweg-de Vries and the regularized long wave equations. SIAM J. Math. Anal., 23:923-940.

[3] Bock, T.L., Kruskal, D., 1979. A two Miura transformation of the Benjamin-Ono equation. Phys. Lett., 74:173-176.

[4] Bu, C., 1995. Modified Korteweg-de Vries equation with generalized function as initial values. J. Math. Phys., 36:3454-3460.

[5] Colombeau, J.F., 1983. A multiplication of distributions. J. Math. Anal. Appl., 94:96-115.

[6] Colombeau, J.F., 1984. New Generalization Functions and Multiplication of Distribution. North Holland Math. Studies. North Holland, Amsterdam.

[7] Colombeau, J.F., 1990. Multiplication of Distributions. Bulletin in A.M.S., 23:251-268.

[8] Colombeau, J.F., 1991. Multiplication of Distributions. A Tool in Applied Mathematics Engineer and Physics. Notes, Ecole Normalesuperieure de Lyon, France.

[9] Iorio, R.J., 1986. On the cauchy problem for the Benjamin-Ono equation. Comm. P. D. E., 11:1031-1081.

[10] Kenig, C.E., Ponce, G., Vega, L., 1994. On the generalized Benjamin-Ono equation. Trans A. M. S., 342:155-172.

[11] Nakamura, A., 1979. Bäcklund transform and conservation laws of the Benjamin-Ono equation. J. PhYS. Soc., 47:1335-1340.

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