Solution of the nonlinear equation of a divergent type in the corner point domain

TL;DR

This paper introduces an algorithm for generating exact solutions to nonlinear partial differential equations of divergent type, focusing on solutions' smoothness in corner domains and utilizing a new class of special functions.

Contribution

It presents a novel algorithm for exact solutions of nonlinear PDEs in corner domains, addressing solution smoothness and introducing new special functions.

Findings

Solutions with unlimited derivatives in corner domains are constructed.

The properties of solution smoothness in corner point domains are analyzed.

A new class of special functions is developed for these solutions.

Abstract

The algorithm for generation of exact solutions of the nonlinear equation in partial derivatives of a divergent type which is included in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schr\"odinger equation) has been suggested. The properties of smoothness of solutions in domains with corner points (piecewise smooth boundary) have been considered. The solutions with unlimited derivatives in the corner point domain have been presented on the basis of a new class of special functions.