Formal exact operator solutions to nonlinear differential equations

TL;DR

This paper presents explicit operator-based solutions for nonlinear differential equations, providing both chronological and non-chronological forms, enhancing the analytical tools for solving complex systems of ODEs and PDEs.

Contribution

It introduces compact, explicit operator solutions for nonlinear differential equations, including variants without chronologization, advancing the theoretical framework for such problems.

Findings

Explicit solutions in the form of chronological operator exponents

Non-chronological operator exponent solutions proposed

Applicable to general systems of nonlinear ODEs and PDEs

Abstract

The compact explicit expressions for formal exact operator solutions to Cauchy problem for sufficiently general systems of nonlinear differential equations (ODEs and PDEs) in the form of chronological operator exponents are given. The variant of exact solutions in the form of ordinary (without chronologization) operator exponents are proposed.