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

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 $$\beta $$ -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.