Algebraic Approaches to the geopotential Forecast and Nonlinear MHD Equations

TL;DR

This paper develops algebraic methods to derive explicit exact solutions with multiple parameters for the geopotential forecast and nonlinear magnetohydrodynamics equations, advancing analytical approaches in fluid dynamics and geophysical modeling.

Contribution

It introduces novel algebraic techniques inspired by previous work to find explicit solutions for complex nonlinear equations in geophysics and MHD.

Findings

New explicit solutions with multiple parameters for geopotential forecast.

Analytical solutions for nonlinear magnetohydrodynamics equations.

Enhanced understanding of solution structures in fluid and geophysical equations.

Abstract

In this paper, we use various anstazes motivated from our earlier works on transonic gas flows, boundary layer problems and Navier-Stokes equations to find new explicit exact solutions with multiple parameter functions for the equation of geopotential forecast and the equations of nonlinear magnetohydrodynamics.