Variable Coefficient KdV Equations and Waves in Elastic Tubes
نویسندگان
چکیده
We present a simplified one-dimensional model for pulse wave propagation through fluid-filled tubes with elastic walls, which takes into account the elasticity of the wall as well as the tapering effect. The spatial dynamics in this model is governed by a variable coefficient KdV equation with conditions given at the inflow site. We discuss an existence theory for the associated evolution equation, based on a semilinear Hille-Yosida theory, which was previously developed for the classical KdV equation.
منابع مشابه
Application of the Kudryashov method and the functional variable method for the complex KdV equation
In this present work, the Kudryashov method and the functional variable method are used to construct exact solutions of the complex KdV equation. The Kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.
متن کاملMulti-soliton of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and KdV equation
A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...
متن کاملWeakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation
In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly nonlinear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg–de Vries (KdV) equation. A progressive wave type of solution, which sati...
متن کاملA KdV-like advection-dispersion equation with some remarkable properties
We discuss a new non-linear PDE, ut + (2uxx/u)ux = uxxx , invariant under scaling of dependent variable and referred to here as SIdV. It is one of the simplest such translation and space-time reflection-symmetric first order advection-dispersion equations. This PDE (with dispersion coefficient unity) was discovered in a genetic programming search for equations sharing the KdV solitary wave solu...
متن کاملSolitary water wave interactions
Our concern in this talk is the problem of free surface water waves, the form of solitary wave solutions, and their behavior under collisions. Solitary waves for the Euler equations have been described since the time of Stokes. In a long wave perturbation regime they are well described by single soliton solutions of the Korteweg deVries equation (KdV). It is a famous result that multiple solito...
متن کامل