CLC number: O13
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 0
Clicked: 6509
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.
@article{title="Generalized solutions to the Benjamin-Ono equations in sense of Colombeau",
author="JIN Xiao-gang, YANG Jian-gang, LIN Jie",
journal="Journal of Zhejiang University Science A",
volume="5",
number="11",
pages="1466-1470",
year="2004",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2004.1466"
}
%0 Journal Article
%T Generalized solutions to the Benjamin-Ono equations in sense of Colombeau
%A JIN Xiao-gang
%A YANG Jian-gang
%A LIN Jie
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 11
%P 1466-1470
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.1466
TY - JOUR
T1 - Generalized solutions to the Benjamin-Ono equations in sense of Colombeau
A1 - JIN Xiao-gang
A1 - YANG Jian-gang
A1 - LIN Jie
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 11
SP - 1466
EP - 1470
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.1466
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.
[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.
Open peer comments: Debate/Discuss/Question/Opinion
<1>