Laws of general solutions of mathematical physics equations

In this paper, the general solutions of five important mathematical physics equations are obtained for the first time, using the Z transformations that we have previously proposed. These five equations are Poisson equation, wave equation, Helmholtz equation, heat equation and Schrödinger equation. According to the general solutions, we also obtain exact solutions of these equations with general significance for the definite solution problems. These new findings not only deepen our understanding of the general solutions of mathematical physics equations, but will also have a positive impact on the development of thermodynamics, optics, acoustics, electrodynamics, statistical mechanics, quantum mechanics and other disciplines.

Authors

Publication Details

Journal
Partial Differential Equations in Applied Mathematics
Published
2024-12-13
DOI
https://doi.org/10.1016/j.padiff.2024.101025
Citations
2
Primary Topic
Differential Equations and Numerical Methods
Type
article
Field-Weighted Citation Impact
1.46
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article

Laws of general solutions of mathematical physics equations

Hong Lai Zhu
2 citations
Partial Differential Equations in Applied Mathematics
Differential Equations and Numerical Methods
1.46
article

Laws of general solutions of mathematical physics equations

Hong Lai Zhu
article en
2 citations

Abstract

In this paper, the general solutions of five important mathematical physics equations are obtained for the first time, using the Z transformations that we have previously proposed. These five equations are Poisson equation, wave equation, Helmholtz equation, heat equation and Schrödinger equation. According to the general solutions, we also obtain exact solutions of these equations with general significance for the definite solution problems. These new findings not only deepen our understanding of the general solutions of mathematical physics equations, but will also have a positive impact on the development of thermodynamics, optics, acoustics, electrodynamics, statistical mechanics, quantum mechanics and other disciplines.

Partial Differential Equations in Applied MathematicsVol. 13
Openalex Percentile: Top 17%
Differential Equations and Numerical Methods
1.46
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