On the Cauchy Problem for the Korteweg–de Vries Equation with Steplike Finite-gap Initial Data I. Schwarz-type Perturbations
نویسنده
چکیده
We solve the Cauchy problem for the Korteweg–de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finitegap potentials under the assumption that the mutual spectral bands either coincide or are disjoint.
منابع مشابه
On the Cauchy Problem for the Korteweg–de Vries Equation with Steplike Finite-gap Initial Data I. Schwartz-type Perturbations
We solve the Cauchy problem for the Korteweg–de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finitegap potentials under the assumption that the respective spectral bands either coincide or are disjoint.
متن کاملOn the Cauchy Problem for the Korteweg–de Vries Equation with Steplike Finite-Gap Initial Data II. Perturbations with Finite Moments
We solve the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.
متن کاملOn the Cauchy Problem for the Modified Korteweg–de Vries Equation with Steplike Finite-Gap Initial Data
We solve the Cauchy problem for the modified Korteweg–de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.
متن کاملForced oscillations of a damped Korteweg-de Vries equation on a periodic domain
In this paper, we investigate a damped Korteweg-de Vries equation with forcing on a periodic domain $mathbb{T}=mathbb{R}/(2pimathbb{Z})$. We can obtain that if the forcing is periodic with small amplitude, then the solution becomes eventually time-periodic.
متن کاملNew analytical soliton type solutions for double layers structure model of extended KdV equation
In this present study the double layers structure model of extended Korteweg-de Vries(K-dV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma model. Then by using of new analytical method we obtain the new exact solitary wave solutions of this equation. Double layer is a structure in plasma and consists of two p...
متن کامل