Exact Solutions of a Remarkable Fin Equation

TL;DR

This paper derives exact solutions for a special nonlinear fin equation using classical and modern symmetry-based methods, enhancing understanding of its mathematical properties.

Contribution

It introduces a set of exact solutions for a remarkable fin equation through various advanced symmetry techniques, expanding the solution space for this class of equations.

Findings

Multiple exact solutions obtained using Lie symmetry and modern methods.

Demonstrates the effectiveness of combining classical and modern techniques.

Provides new insights into the structure of the fin equation.

Abstract

A model "remarkable" fin equation is singled out from a class of nonlinear (1+1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both classical Lie algorithm and different modern techniques (functional separation of variables, generalized conditional symmetries, hidden symmetries etc).