We study the stability of the steady waves forced by a moving localised pressure disturbance in water of finite depth. The steady waves take the form of a downstream wavetrain for subcritical flow, but for supercritical flow there is a solution branch for each specified forcing term, which has two localised solitarylike solutions for each Froude number, a small-amplitude and a large-amplitude s...

As part of our efforts to unveil extragalactic large-scale structures behind the southern Milky Way, we here present redshifts for 764 galaxies in the Hydra/Antlia, Crux and Great Attractor region (266◦ ≤ l ≤ 338◦, | b | ∼ 10 ◦), obtained with the Meudon-ESO Fibre Object Spectrograph (MEFOS) at the 3.6-m telescope of ESO. The observations are part of a redshift survey of partially obscured gala...

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

Abstract. We study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlevé I hierarchy. It is shown that this solution gives a valid asympto...

The basic theory of internal solitary waves is reviewed, with the main emphasis on applications to the many observations of such waves in shallow coastal seas, fjords, lakes and in the atmospheric boundary layer. Commencing with the equations of motion for an inviscid, incompressible density-stratified fluid, we describe asymptotic reductions to model long-wave equations, including the well-kno...

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV-K(m, n) equation. Furthermore for the mixed models of linear and nonli...

We discuss several PT -symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT -symmetric deformations of the supersymmetric Korteweg-de Vries equation. Some of these new models are mere fermionic extensions of the former in the sense that they are formulated in terms of superspace valued superfields containing bosonic and fermioni...

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...

In this article we study three capillary compressible models (the classical local Navier-Stokes-Korteweg system and two non-local models) for large initial data, bounded away from zero, and with a reference pressure state ρ̄ which is not necessarily stable (P (ρ̄) can be non-positive). We prove that these systems have a unique local in time solution and we study the convergence rate of the soluti...