New classes of symmetries for partial differential equations
From MaRDI portal
Publication:3822890
DOI10.1063/1.527974zbMath0669.58037OpenAlexW2046601112MaRDI QIDQ3822890
Gregory J. Reid, Sukeyuki Kumei, George W. Bluman
Publication date: 1988
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.527974
Wave equation (35L05) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)
Related Items
Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation, Application of symmetry analysis to viscoelastic fluid model, Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation, On Symmetries and Conservation Laws for a Generalized Fisher–Kolmogorov–Petrovsky–Piskunov Equation, A symmetry-based method for constructing nonlocally related partial differential equation systems, Symmetry-based algorithms to relate partial differential equations: I. Local symmetries, Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries, Potential symmetries and invariant solutions for the generalized one-dimensional Fokker-Planck equation, Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation, Transformation properties of a variable-coefficient Burgers equation, Symmetry of stochastic non-variational differential equations, Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion, Exact solutions of a Black-Scholes model with time-dependent parameters by utilizing potential symmetries, Derivation of conservation laws from nonlocal symmetries of differential equations, New explicit solutions of the Burgers equation, Applications of Integrable Nonlinear Diffusion Equations in Industrial Modelling, Analysis of modified Painlevé-Ince equations, On Nonlocal Symmetries, Nonlocal Conservation Laws and Nonlocal Transformations of Evolution Equations: Two Linearisable Hierarchies, Finding abstract Lie symmetry algebras of differential equations without integrating determining equations, Surface-concentration-dependent nonlinear diffusion, The use of factors to discover potential systems or linearizations, Some relations between symmetries of nonlocally related systems, Symbolic Computation of Nonlocal Symmetries and Nonlocal Conservation Laws of Partial Differential Equations Using the GeM Package for Maple, Potential symmetries and associated conservation laws to Fokker-Planck and Burgers equation, Conservation laws for one-layer shallow water wave systems, New similarity reductions of the Boussinesq equation, Symmetries of the Ablowitz–Kaup–Newell–Segur hierarchy, Evolution of contact and weak discontinuity waves in two phase drift flux model, Potential nonclassical symmetries and solutions of fast diffusion equation, Nonlocal symmetries of the Camassa-Holm type equations, Symmetry reductions, generalized solutions and dynamics of wave profiles for the \((2+1)\)-dimensional system of Broer-Kaup-Kupershmidt (BKK) equations, Nonlocal symmetries classifications and exact solution of Chaplygin gas equations, Nonlocal Extensions of Similarity Methods, Nonclassical Potential System Approach for a Nonlinear Diffusion Equation, Conservation laws and some new exact solutions for traffic flow model via symmetry analysis, Symmetries and conservation laws of a KdV6 equation, Painlevé test and exact similarity solutions of a class of nonlinear diffusion equations, Generation solutions algorithms for the class of inhomogeneous nonlinear diffusion equations, EXPLICIT SOLUTIONS TO THE KAUP–KUPERSHMIDT EQUATION VIA NONLOCAL SYMMETRIES, General similarity reductions of a family of Cahn-Hilliard equations, Nonclassical potential symmetries for the Burgers equation, Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach, Symmetry analysis for a class of nonlinear dispersive equations, How symmetries yield non-invertible mappings of linear partial differential equations, Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation, Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities, A (1+1)-dimensional integrable system with fifth order spectral problems and four dispersion relations, Special types of solitons and breather molecules for a (2+1)-dimensional fifth-order KdV equation, Nonlocal symmetries and nonlocal conservation laws of Maxwell’s equations, A new symmetry-based method for constructing nonlocally related PDE systems from admitted multi-parameter groups, Nonlocal symmetries and explicit solutions of the Boussinesq equation, New explicit solutions of Einstein equations in the framework of GAP Theory, Nonlocal symmetries of systems of evolution equations, Equivalence of conservation laws and equivalence of potential systems, Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations, Nonclassical potential symmetries and invariant solutions of heat equation, Conservation laws and potential symmetries of linear parabolic equations, Classical and potential symmetries for a generalized Fisher equation, On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations, Partial symmetry of initial value problems, Similarity reduction, nonlocal and master symmetries of sixth order Korteweg–deVries equation, On relation between potential and contact symmetries of evolution equations, Invariant analysis and conservation laws of the time-fractional \(b\)-family peakon equations, Symmetry properties for a generalised thin film equation, Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification, [SADE a Maple package for the symmetry analysis of differential equations], Nonlocal symmetries and recursion operators: Partial differential and differential-difference equations, Analytical reduction for a concentration dependent diffusion problem, Symbolic computation of local symmetries of nonlinear and linear partial and ordinary differential equations, Similarity solutions of the Burgers equation with linear damping., A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations, Nonlocal symmetries and formulae for generation of solutions for a class of diffusion-convection equations, Computation of fluxes of conservation laws, Potential systems for PDEs having several conservation laws, Relevance of symmetry methods in mechanics of materials, Similarity: Generalizations, applications and open problems, Symmetries, conservation laws, and cohomology of Maxwell's equations using potentials, Nonlocal symmetries of evolution equations, Classification of local and nonlocal symmetries of fourth-order nonlinear evolution equations, Second-order approximate symmetry classification and optimal system of a class of perturbed nonlinear wave equations, Similarity solutions for two-dimensional weak shock waves, Invariant solutions and conservation laws to nonconservative FP equation, Differential Equations Invariant Under Conditional Symmetries, Field theories with higher-group symmetry from composite currents, Nonlocal symmetries of the KdV equation, Generalized symmetries for the ideal MHD equations, Construction of Partial Differential Equations with Conditional Symmetries, Nonclassical Symmetries for a Class of Reaction-Diffusion Equations: the Method of Heir-Equations, Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations, Potential symmetries and conservation laws for generalized quasilinear hyperbolic equations, Conditional Lie-Bäcklund symmetries and functionally generalized separable solutions to the generalized porous medium equations with source, Conservation laws for the Black-Scholes equation, Nonlocal ansätze, reduction and some exact solutions for the system of the van der Waals equations, Nonclassical symmetries of a power law Harry Dym equation, Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source, On locally and nonlocally related potential systems, Conditional Lie-Bäcklund Symmetries and Invariant Subspaces to Nonlinear Diffusion Equations with Convection and Source, Nonlocal symmetries of the system of chemotaxis equations with derivative nonlinearity, Nonlocal transformations with additional variables. Forced symmetries, Nonclassical symmetry reductions of the Boussinesq equation, Group-theoretical framework for potential symmetries of evolution equations, Potential symmetries of inhomogeneous nonlinear diffusion equations, Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution, Separation of variables of a generalized porous medium equation with nonlinear source., Nonlocal symmetries and explicit solutions of the AKNS system, Framework for potential systems and nonlocal symmetries: Algorithmic approach, Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations, Potential symmetry reduction of a convection-dispersion equation with spatial dependent water velocity
Cites Work
