Korteweg–de Vries surfaces

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

A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a densityand current-stratified shear flow with a free surface. All coefficients of this extended Kortewegde 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 whi...

Hugo De Vries

Modal De Vries Algebras

We introduce modal de Vries algebras and develop a duality between the category of modal de Vries algebras and the category of coalgebras for the Vietoris functor on compact Hausdorff spaces. This duality serves as a common generalization of de Vries duality between de Vries algebras and compact Hausdorff spaces, and the duality between modal algebras and modal spaces.

The Improved Fractional Sub-equation Method and Its Applications to Nonlinear Fractional Partial Differential Equations

The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinear fractional partial differential equations. By means of this method, the space-time fractional generalized Hirota-Satsuma coupled Kortewegde Vries equations are successfully solved. As a result, three types...

Coupled Korteweg-de Vries equations

When a system supports two distinct long-wave modes with nearly coincident phase speeds, the weakly nonlinear and linear dispersion unfolding generically leads to two coupled Korteweg-de Vries equations. In this paper, we review the derivation of such systems in stratified fluids, extending previous studies by allowing for background shear flows. Coupled Korteweg-de Vries systems have very rich...