Modified Korteweg-deVries Equation and scattering theory
نویسندگان
چکیده
منابع مشابه
Acoustic Scattering and the Extended Korteweg deVries Hierarchy
The acoustic scattering operator on the real line is mapped to a Schrödinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scatterin...
متن کاملAnalytical and Numerical Studies of Weakly Nonlocal Solitary Waves of the Rotation-Modified Korteweg-deVries Equation
A century ago, the Korteweg-deVries (KdV) equation was derived as a model for weakly nonlinear long waves propagating down a channel when cross-channel and depth variations are sufficiently weak. In this article, we study the steadily-translating coherent structures of a generalization of this equation, the Rotation-Modified Korteweg-deVries equation, which applies when Coriolis forces are sign...
متن کاملVariational Method for Studying Solitons in the Korteweg-DeVries Equation
We use a variational method based on the principle of least action to obtain approximate time-dependent single soliton solutions to the KdV equation. A class of trial variational functions of the form u(x, t) = −A(t) exp [ −β(t) |x− q(t)| ] , with n a continuous real variable, is used to parametrize timedependent solutions. We find that this class of trial functions leads to soliton-like soluti...
متن کاملPole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation
The real, nonsingular elliptic solutions of the Korteweg-deVries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is governed by a dynamical system with a constraint. This constraint is shown to be solvable for any finite number of poles located in the fundamental domain of the elliptic function, often in many different ways. Specia...
متن کاملFive Regimes of the Quasi-Cnoidal, Steadily Translating Waves of the Rotation-Modified Korteweg-deVries (“Ostrovsky”) Equation
The Rotation-Modified Korteweg-deVries (RMKdV) equation differs from the ordinary KdV equation only through an extra undifferentiated term due to Coriolis force. This article describes the steadily-travelling, spatially-periodic solutions which have peaks of identical size. These generalize the “cnoidal” waves of the KdV equation. There are five overlapping regimes in the parameter space. We de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1972
ISSN: 0386-2194
DOI: 10.3792/pja/1195519590