Partial Differential Equations and Symmetry
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: closed (31 March 2026) | Viewed by 666
Special Issue Editors
Interests: soliton and integrable system; mathematical mechanization and mathematical physics; fractional differential equation and its applications
Special Issues, Collections and Topics in MDPI journals
Interests: soliton and integrable system; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Partial differential equations, including special types of differential-integral, lattice (semi-discrete or fully discrete), and fractional-order equations, are very important and have been widely used in many fields such as engineering, physics, fluid mechanics, finance, biology, etc. Some famous partial differential equations include the following: Lagrange equation, Laplace equation, Poisson equation, Maxwell’s equations, Helmholtz equation, Navier–Stokes equation, Schrödinger equation, heat equation, wave equation, reaction–diffusion equation, soliton equation, etc.
This Special Issue aims to enhance our understanding of various analytical and numerical methods, symmetry analysis, and solutions for partial differential equations, as well as the symmetry that arises in solutions. The goal of this Special Issue is to explore new results and directions in partial differential equations and symmetry, highlight the important role of symmetry in partial differential equations, and establish new theoretical foundations for related field applications.
The scope of this Special Issue includes, but is not limited to, the following: symmetry method, analytical method, Lie group method, symmetry analysis, numerical algorithm, symmetry property, separation of variables method, symmetry reduction, exact solution, approximate solution, symmetry structure, spectral method, Fourier transform, Laplace transform, inverse scattering transform, finite difference method, finite element method, Riemann–Hilbert method, Darboux transformation, Bilinear method, function expansion method, Green’s function method, characteristic line method, variational method, integral transformation method, physics informed neural method, and other methods related to symmetry for partial differential equations.
We look forward to receiving your contributions.
Prof. Dr. Sheng Zhang
Dr. Bo Xu
Guest Editors
Manuscript Submission Information
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Keywords
- partial differential equations
- analytical method and numerical algorithm
- symmetry analysis
- inverse scattering transform
- finite difference method
- Riemann–Hilbert method
- function expansion method
- integral transformation method
- physics-informed neural method
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