Grimshaw, R., Pelinovsky, E. and Poloukhina, O. (2002) Higher-Order Korteweg-de Vries Models for Internal Solitary Waves in a Stratified Shear Flow with a Free Surface. Nonlinear Processes in Geophysics, 9, 221-235.
https://doi.org/10.5194/npg-9-221-2002

has been cited by the following article:

• TITLE: The Dispersion Relation of Internal Wave Extended-Korteweg-de Vries Equation in a Two-Layer Fluid

  AUTHORS: Pingping Feng, Xianghua Meng

  KEYWORDS: Ocean Internal Waves, Dispersion Relation, Extended-Korteweg-de Vries Equation, Poincaré-Lighthill-Kuo Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.5, May 27, 2021

  ABSTRACT: To understand the characteristics of ocean internal waves better, we study the dispersion relation of extended-Korteweg-de Vries (EKdV) equation with quadratic and cubic nonlinear terms in a two-layer fluid by using the Poincaré-Lighthill-Kuo (PLK) method which is one of the perturbation methods. Starting from the partial differential equation, the PLK method can be used to solve the dispersion relation of the equation. In this paper, we use PLK method to solve the equation and derive the dispersion relation of EKdV equation which is related to wave number and amplitude. Based on the dispersion relation obtained in this paper, the expressions of group velocity and phase velocity of the equation are obtained. Under the actual hydrological data, the influence of hydrological parameters on the dispersion relation for descending internal wave is discussed. It is hope that the obtained results will be helpful to the study of energy transfer and other internal wave parameters in the future.