This article is concerned with a Kuramoto–Sivashinsky-Korteweg-de Vries equation in bounded interval. The as well one of the boundary conditions are supposed to be subject presence parameter $ \nu> 0 $. Moreover, this specific condition has time-delay effect. As \nu tends zero, we show that can obtain findings [4,58] concerning two Korteweg–de equations. Indeed, able retrieve well-posedness ...

Abstract. Purely dispersive equations, such as the Korteweg-de Vries and the nonlinear Schrödinger equations in the limit of small dispersion, have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral ...

We establish the semiclassical limit of the one-dimensional defocusing cubic nonlinear Schrödinger (NLS) equation. Complete integrability is exploited to obtain a global characterization of the weak limits of the entire NLS hierarchy of conserved densities as the field evolves from reflectionless initial data under all the associated commuting flows. Consequently, this also establishes the zero...

— The conservation and convergence properties o f spectral Fourier methods for the numerical approximation o f the Korteweg-de Vries équation are analyzed. It is proven thaï the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point ofview. This resuit provides a précise mathematica...

(Received ?? and in revised form ??) It is well-known that transcritical flow over a localised obstacle generates upstream and downstream nonlinear wavetrains. The flow has been successfully modeled in the framework of the forced Korteweg-de Vries equation, where numerical and asymptotic analytical solutions have shown that the upstream and downstream nonlinear wavetrains have the structure of ...