Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation

Daxin Wu; Shih-Liang Wen

Rendiconti del Seminario Matematico della Università di Padova (1991)

  • Volume: 86, page 89-109
  • ISSN: 0041-8994

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Wu, Daxin, and 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 86 (1991): 89-109. <http://eudml.org/doc/108244>.

@article{Wu1991,
author = {Wu, Daxin, Wen, Shih-Liang},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {existence; uniqueness; initial problem},
language = {eng},
pages = {89-109},
publisher = {Seminario Matematico of the University of Padua},
title = {Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation},
url = {http://eudml.org/doc/108244},
volume = {86},
year = {1991},
}

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
PB - Seminario Matematico of the University of Padua
VL - 86
SP - 89
EP - 109
LA - eng
KW - existence; uniqueness; initial problem
UR - http://eudml.org/doc/108244
ER -

References

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  2. [2] R.A. Adams, Sobolev Spaces, Academic Press, New York (1975). Zbl0314.46030MR450957
  3. [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. Zbl0634.35066MR904224
  4. [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. Zbl0639.35077MR1017499
  5. [5] P. Guo, Global solutions of the generalized KdV equation, Acta Math. Sinica, 25, n. 6 (1983) (in Chinese). 
  6. [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. Zbl0217.25004
  7. [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. Zbl26.0881.02JFM26.0881.02
  8. [8] R.J. Leveque, On the interaction of nearly equal solitons in the KdV equation, SIAM J. Appl. Math., 47, n. 2 (1987). Zbl0637.35078MR881349
  9. [9] R.M. Miura, The Korteweg-de Vries equation: A survey of results, SIAM Rev., 18, n. 3 (1976), pp. 412-459. Zbl0333.35021MR404890
  10. [10] M. Schwartz jr., Periodic solutions of Kadomtsev-Petviashvili equation, Advances in Math., 66 (1987), pp. 217-233. Zbl0659.35084MR915855
  11. [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). Zbl0721.35071
  12. [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. Zbl0737.35112MR1113410
  13. [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. Zbl1201.35174

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