Monge equation of arbitrary degree in 1 + 1 space

TL;DR

This paper explores solutions to the Monge equation of arbitrary degree in 1+1 space, linking it to functional equations involving four functions, and provides explicit solutions for some cases.

Contribution

It introduces a novel connection between high-order Monge equations and functional equations, offering explicit solutions for certain instances.

Findings

Explicit solutions for specific cases of the Monge equation of arbitrary degree.

Establishment of a link between Monge equations and functional equations with four functions.

New methods for solving high-order nonlinear differential equations.

Abstract

Solution of Monge equation of arbitrary degree (non linear differential equation n-orden) is connected with solution of functional equation for 4 functions with 4 different arguments. Some number solutions of this equation is represented in explicit form.