NLS equation of internal waves in weakly stratified ocean

Xu Zhao-ting; Lou Shun-li; Tian Ji-wei; Samuel Shan-pu Shen

doi:10.1007/BF02850368

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NLS equation of internal waves in weakly stratified ocean

Updated：2023-05-16

- NLS equation of internal waves in weakly stratified ocean
- Journal of Oceanology and Limnology Vol. 14, Issue 2, Pages: 121-127(1996)
- Affiliations：
  
  1. Physical Oceanography Laboratory and Institute of Physical Oceanography
  2. Department of Mathematics and Applied Mathematics Institute University of Alberta
- Author bio：
- Funds：
- DOI：10.1007/BF02850368
  CLC：
- Online First：31 January 2013，
  
  Published：1996
- Accepted：
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Zhao-ting, X., Shun-li, L., Ji-wei, T. et al. NLS equation of internal waves in weakly stratified ocean., Chin. J. Ocean. Limnol. 14, 121–127 (1996). https://doi.org/10.1007/BF02850368
DOI：

Zhao-ting, X., Shun-li, L., Ji-wei, T. et al. NLS equation of internal waves in weakly stratified ocean., Chin. J. Ocean. Limnol. 14, 121–127 (1996). https://doi.org/10.1007/BF02850368 DOI：

摘要

Abstract

The NLS (Non-Linear Schrödinger) equation of internal waves in a weakly stratified ocean is derived in phase coordinates in terms of the RPM (Reductive Perturbation Method). It was shown that whenAB>0 there exist modulation forms of envelope soliton anddn

and that whenAB<0 there are three modulation forms: dark soliton

sn andcn Only if {ie121-1} the side-band perturbation

is stable

otherwise unstable. For the stable side-band perturbation there exists a modulation form ofKdV soliton.

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Keywords

references

Davey, A. & Stewartson, K., 1974. On three-dimensional packets of surface wave.Proc. Roy. Soc. London. A338: 101–110.

Dysthe, K. B., 1979. Note on a modification to the nonlinear Schrodinger equation for application to deep water waves.Proc. roy. Soc. London. A369: 105–114.

Hui, W. H., Hamilton, J., 1979. Exact solution of a three-dimensional nonlinear Schrodinger equation applied to gravity wave.J. Fluid Mech. 93: 117–132.

Leonov, A. Y., Miropolsky, U. Z., 1974.Reports of Scientific Academy, U. S. S. R.,218(6): 1287–1290. (in Russian)

Leonov, A. Y., Miropolsky, U. Z., 1975. Short wave approximation in the theory of nonlinear steady interal gravity waves.Phys. Atmo. and Ocean 11(11): 1169–1178. (in Russian)

Xu Zhaoting, Shen, S. S., 1991. Nonlinear modulation of the short internal waves in the weakly stratified ocean.J. Chin. Ocean. Limn. 9: 364–374.

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