Multiple Parameter Function Approaches to the Equations of Dynamic Convection in a Sea

TL;DR

This paper introduces multiple parameter function schemes and symmetry transformations to derive new explicit solutions for the equations of dynamic convection in a sea, advancing analytical methods in geophysical fluid dynamics.

Contribution

It presents novel multiple parameter function approaches and symmetry techniques to solve the equations of dynamic convection, providing new explicit solutions in geophysics.

Findings

Derived families of explicit solutions using multiple parameter functions.

Applied symmetry transformations to simplify solution derivation.

Enhanced analytical methods for modeling sea convection.

Abstract

One of the most important topics in geophysics is to study convection in a sea. Based on the algebraic characteristics of the equations of dynamic convection in a sea, we introduce various schemes with multiple parameter functions to solve these equations and obtain families of new explicit exact solutions with multiple parameter functions. Moreover, symmetry transformations are used to simplify our arguments.