# A general nonlocal variable coefficient KdV equation with shifted parity and delayed time reversal

A general nonlocal variable coefficient KdV equation with shifted parity and delayed time reversal A general nonlocal time-dependent variable coefficient KdV (VCKdV) equation with shifted parity and delayed time reversal is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a $$\beta$$ β -plane. A special transformation is established to change it into a nonlocal constant coefficient KdV (CCKdV) equation with shifted parity and delayed time reversal. Making advantage of this transformation, exact solutions of the nonlocal CCKdV equation can be utilized to construct exact solutions of the nonlocal VCKdV equation. Two kinds of nonlinear wave excitations are presented explicitly and graphically. Though they possess very simple wave profiles, they can move in abundant ways due to the arbitrary time-dependent functions in their exact solutions, and can be used to model various blocking events in climate disasters. It is demonstrated that a special approximate solution of the original stream functions can capture a kind of two correlated dipole blocking events with a lifetime. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

# A general nonlocal variable coefficient KdV equation with shifted parity and delayed time reversal

, Volume 94 (1) – Jun 5, 2018
10 pages

/lp/springer_journal/a-general-nonlocal-variable-coefficient-kdv-equation-with-shifted-yh0KLwaVfb
Publisher
Springer Journals
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-018-4386-8
Publisher site
See Article on Publisher Site

### Abstract

A general nonlocal time-dependent variable coefficient KdV (VCKdV) equation with shifted parity and delayed time reversal is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a $$\beta$$ β -plane. A special transformation is established to change it into a nonlocal constant coefficient KdV (CCKdV) equation with shifted parity and delayed time reversal. Making advantage of this transformation, exact solutions of the nonlocal CCKdV equation can be utilized to construct exact solutions of the nonlocal VCKdV equation. Two kinds of nonlinear wave excitations are presented explicitly and graphically. Though they possess very simple wave profiles, they can move in abundant ways due to the arbitrary time-dependent functions in their exact solutions, and can be used to model various blocking events in climate disasters. It is demonstrated that a special approximate solution of the original stream functions can capture a kind of two correlated dipole blocking events with a lifetime.

### Journal

Nonlinear DynamicsSpringer Journals

Published: Jun 5, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations