Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
Rendiconti del Seminario Matematico della Università di Padova, Tome 86 (1991), pp. 89-109. 
@article{RSMUP_1991__86__89_0,
     author = {Wu, Daxin and Wen, Shih-Liang},
     title = {Existence and uniqueness of a periodic solution to the two-dimensional generalized {Korteweg-de} {Vries} equation},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {89--109},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {86},
     year = {1991},
     mrnumber = {1154101},
     zbl = {0754.35152},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1991__86__89_0/}
}
TY  - JOUR
AU  - Wu, Daxin
AU  - Wen, Shih-Liang
TI  - Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 1991
SP  - 89
EP  - 109
VL  - 86
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_1991__86__89_0/
LA  - en
ID  - RSMUP_1991__86__89_0
ER  - 
%0 Journal Article
%A Wu, Daxin
%A Wen, Shih-Liang
%T Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
%J Rendiconti del Seminario Matematico della Università di Padova
%D 1991
%P 89-109
%V 86
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_1991__86__89_0/
%G en
%F RSMUP_1991__86__89_0
Wu, Daxin; Wen, Shih-Liang. Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation. Rendiconti del Seminario Matematico della Università di Padova, Tome 86 (1991), pp. 89-109. http://www.numdam.org/item/RSMUP_1991__86__89_0/

[1] M.J. Ablowitz - H. SEGUR, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981). | MR | Zbl

[2] R.A. Adams, Sobolev Spaces, Academic Press, New York (1975). | MR | Zbl

[3] Y. Chen - S. Wen, Traveling wave solutions to the two-dimensional Korteweg-de Vries equation, J. Math. Anal. Appl., 127, n. 1 (1987), pp. 226-236. | MR | Zbl

[4] Y. Chen - S. Wen, On existence theorems of periodic traveling wave solutions to the two-dimensional Korteweg-de Vries equation, Applicable Analysis, 31 (1988), pp. 1-10. | MR | Zbl

[5] P. Guo, Global solutions of the generalized KdV equation, Acta Math. Sinica, 25, n. 6 (1983) (in Chinese).

[6] B.B. Kadomtsev - V. I. PETVIASHVILI, On the stability of solitary waves in weakly dispersing media, Dokl. Akad. Nauk SSSR, 192 (1970), pp. 753-756. | Zbl

[7] D.J. Korteweg - G. De Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag. (5), 39 (1895), pp. 422-443. | JFM

[8] R.J. Leveque, On the interaction of nearly equal solitons in the KdV equation, SIAM J. Appl. Math., 47, n. 2 (1987). | MR | Zbl

[9] R.M. Miura, The Korteweg-de Vries equation: A survey of results, SIAM Rev., 18, n. 3 (1976), pp. 412-459. | MR | Zbl

[10] M. Schwartz Jr., Periodic solutions of Kadomtsev-Petviashvili equation, Advances in Math., 66 (1987), pp. 217-233. | MR | Zbl

[11] D. Wu - S. Wen, On the interaction of the two nearly equal solitons in the two-dimensional KdV equation, Proceedings of the International Conference on Differential Equations, Columbus, Ohio (1988). | Zbl

[12] D. Wu - S. WEN, A uniqueness theorem for the two-dimensional generalized Korteweg-de Vries equation, J. Math. Anal. Appl., 158, No. 1 (1991), pp. 203-212. | MR | Zbl

[13] N.J. Zabusky - M. D. KRUSKAL, Interactions of solitons in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett., 15 (1965), pp. 240-243.