Abstract
•The generalized modified variable-coefficient KdV equation with external force term (gvcmKdV) describes atmospheric blocking located in the mid-high latitudes over ocean is studied.•The gvcmKdV equation is integrable according to the consistent Riccati expansion solvability under some conditions between variable coefficients.•The gvcmKdV equation is reduced to a third-order nonlinear ordinary differential equation by the classical direct similarity reduction method.•Many novel solitary and periodic wave solutions are obtained.
In this study, the generalized modified variable-coefficient KdV equation with external-force term (gvcmKdV) describing atmospheric blocking located in the mid-high latitudes over ocean is studied for integrability property by using consistent Riccati expansion solvability and the necessary integrability conditions between the function coefficients are obtained. Moreover, several new solutions have been constructed for the gvcmKdV. Additionally, the classical direct similarity reduction method is used to reduce the gvcmKdV to a nonlinear ordinary differential equation. Building on the solutions given in the previous literature for the reduced equation, many novel solitary and periodic wave solutions have been obtained for the gvcmKdV.