Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

By Roger Grimshaw, Efim N. Pelinovsky, O. Poloukhina. 2002

154 citations recorded by the source corpus.

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.

Subfields: Atmospheric Science, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1367b3fe0f7b87a8cf46b54fee1b757eea6ff01a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atmospheric Science

1. Roger Grimshaw
2. W. Melville

In Oceanography

1. W. Melville
2. K. Helfrich
3. Roger Grimshaw
4. Gennady El
5. Mark A. Hoefer

In Statistical and Nonlinear Physics

1. W. Melville
2. K. Helfrich
3. Roger Grimshaw
4. Gennady El
5. Mark A. Hoefer

Citations in the corpus

• Internal Solitary Waves (2003, methodology): “Hamiltonian), it is necessary that δ = 2γ which is generally not the case (see [14]).”
• Long Nonlinear Internal Waves (2006, background): “The cubic term in Equation 1 is O(α2), and thus Equation 1 should formally include additional O(β2) and O(αβ) terms to give a higher-order KdV equation valid to O(α2) (Grimshaw et al. 2002, Koop & Butler 1981, Lamb & Yan 1996).”