Potential symmetries and invariant solutions for the generalized one-dimensional Fokker-Planck equation

DOI10.1016/S0378-4371(01)00496-4zbMath1098.82611MaRDI QIDQ5956516

S. F. Abdul-Aziz, M. H. M. Moussa, A. H. Khater

Publication date: 20 February 2002

Published in: Physica A (Search for Journal in Brave)

Mathematics Subject Classification ID

Nonlinear higher-order PDEs (35G20) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items

Symmetry of stochastic non-variational differential equations ⋮ Conservation laws for one-layer shallow water wave systems ⋮ A 3D vortex formed by trajectories of the Navier–Stokes equation ⋮ A Chebyshev spectral collocation method for solving Burgers'-type equations ⋮ Conservation laws and exact solutions for some nonlinear partial differential equations ⋮ Group-theoretical framework for potential symmetries of evolution equations ⋮ Potential symmetry reduction of a convection-dispersion equation with spatial dependent water velocity ⋮ Potential symmetries and invariant solutions for the inhomogeneous nonlinear diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the weak symmetry groups of partial differential equations
• The use of factors to discover potential systems or linearizations
• Symmetry classes of Fokker-Planck-type equations
• Lie symmetries of some equations of the Fokker–Planck type
• Ovsiannikov’s method and the construction of partially invariant solutions
• New classes of symmetries for partial differential equations
• Generalised symmetries of Fokker-Planck-type equations
• Applications of the general similarity solution of the heat equation to boundary-value problems
• Direct Construction of Conservation Laws from Field Equations
• Potential symmetries and solutions by reduction of partial differential equations
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries