Modified Korteweg-de Vries equation as a system with benign ghosts

نویسندگان

چکیده

We consider the modified Korteweg-de Vries equation, uxxx + 6u2ux ut = 0, and explore its dynamics in spatial direction. Higher x derivatives bring about ghosts. argue that these ghosts are benign, i.e., classical of this system does not involve a blow-up. This probably means associated quantum problem is also well defined.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Unbounded Solutions of the Modified Korteweg-De Vries Equation

Abstract We prove local existence and uniqueness of solutions of the focusing modified Korteweg de Vries equation ut+u 2 ux+uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a gener...

متن کامل

Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach

A proper bilinear form is proposed for the N = 1 supersymmetric modified Korteweg-de Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it.

متن کامل

Korteweg-de Vries Equation in Bounded Domains

where μ, ν are positive constants. This equation, in the case μ = 0, was derived independently by Sivashinsky [1] and Kuramoto [2] with the purpose to model amplitude and phase expansion of pattern formations in different physical situations, for example, in the theory of a flame propagation in turbulent flows of gaseous combustible mixtures, see Sivashinsky [1], and in the theory of turbulence...

متن کامل

New Positon, Negaton, and Complexiton Solutions for a Coupled Korteweg--de Vries -- Modified Korteweg--de Vries System

On the exact solutions of integrable models, there is a new classification way recently based on the property of associated spectral parameters [1]. Negatons, related to the negative spectral parameter, are usually expressed by hyperbolic functions, and positons are expressed by means of trigonometric functions related to the positive spectral parameters. The so-called complexiton, which is exp...

متن کامل

Numerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations

Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accur...

متن کامل

ذخیره 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: Acta Polytechnica

سال: 2022

ISSN: ['1210-2709', '1805-2363']

DOI: https://doi.org/10.14311/ap.2022.62.0190