The general solutions of some nonlinear second order PDEs.I. Two independent variables, constant parameters

TL;DR

This paper presents formal general solutions for 80 types of second order nonlinear PDEs with two variables, demonstrating the use of order reduction and Maple implementation to solve various PDEs.

Contribution

It introduces a systematic approach using order reduction and Maple procedures to solve and analyze a broad class of nonlinear second order PDEs with constant parameters.

Findings

Classification of solvable PDEs with explicit solutions

Implementation of Maple procedures for PDE solving

Demonstration of order reduction and lifting techniques

Abstract

In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is to show on examples the types of solvable PDEs and what their general solutions look like. The solving strategy, used here, as a rule is the order reduction. The order reduction method is implemented in Maple procedure, which applicable to PDEs of different order with different number of independent variables. Some of given PDEs are solved by order lifting to PDEs, which are solvable by the subsequent order reduction.