Complete group classification of a class of nonlinear wave equations

Abstract

Preliminary group classification became prominent as an approach to symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi and Valenti [J. Math. Phys. 32, 2988-2995] in which partial preliminary group classification of a class of nonlinear wave equations was carried out via the classification of one-dimensional Lie symmetry extensions related to a fixed finite-dimensional subalgebra of the infinite-dimensional equivalence algebra of the class under consideration. In the present paper we implement, up to both usual and general point equivalence, the complete group classification of the same class using the algebraic method of group classification. This includes the complete preliminary group classification of the class and finding Lie symmetry extensions which are not associated with subalgebras of the equivalence algebra. The complete preliminary group classification is based on listing all inequivalent subalgebras of the whole infinite-dimensional equivalence algebra whose projections are qualified as maximal extensions of the kernel algebra. The set of admissible point transformations of the class is exhaustively described in terms of the partition of the class into normalized subclasses. A version of the algebraic method for finding the complete equivalence groups of a general class of differential equations is proposed.

39 pages

References in corpus (11)

• New results on group classification of nonlinear diffusion-convection equations
• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Conservation Laws and Potential Symmetries of Linear Parabolic Equations
• More common errors in finding exact solutions of nonlinear differential equations. I
• Enhanced preliminary group classification of a class of generalized diffusion equations
• Symmetry preserving parameterization schemes
• Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations
• Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities
• Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem
• Point symmetry group of the barotropic vorticity equation
• Theta-functions on T^2-bundles over T^2 with the Euler class zero

Cited by in corpus (36)

• Equivalence transformations in the study of integrability
• Enhanced group classification of Gardner equations with time-dependent coefficients
• Group classification of linear evolution equations
• Group analysis of general Burgers-Korteweg-de Vries equations
• Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
• Lie symmetries of two-dimensional shallow water equations with variable bottom topography
• Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping
• Algebraic method for finding equivalence groups
• Complete point symmetry group of the barotropic vorticity equation on a rotating sphere
• Extended symmetry analysis of generalized Burgers equations
• Group classification of (1+3)-dimensional Schrödinger equations with position dependent mass
• Group classification of variable coefficient generalized Kawahara equations
• Inverse problem on conservation laws
• Singular reduction modules of differential equations
• Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations
• Equivalence groupoids of classes of linear ordinary differential equations and their group classification
• Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
• Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
• Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations
• Group classification of variable coefficient quasilinear reaction-diffusion equations
• Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
• Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations
• Conservative parameterization schemes
• Mapping method of group classification
• Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
• Lie group analysis of a generalized Krichever-Novikov differential-difference equation
• Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation
• Lie reductions and exact solutions of dispersionless Nizhnik equation
• Equivalence groupoid of generalized potential Burgers equations
• Invariant parameterization of geostrophic eddies in the ocean
• Group analysis of Benjamin-Bona-Mahony equations with time dependent coefficients
• Admissible Equivalence Transformations for Linearization of Nonlinear Wave Type Equations
• Classification of scalar second-order differential equations with low-dimensional symmetry groups: The case of free action
• Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivity
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation
• Lie symmetries and similarity solutions for the generalized Zakharov equations