Differential invariants of nonlinear equations \(v_{tt}=f(x,v_{x})v_{xx}+g(x,v_{x})\).

DOI10.1016/S1007-5704(03)00016-9zbMath1035.35081OpenAlexW2016530544MaRDI QIDQ1417830

Nail H. Ibragimov, Mariano Torrisi, Antonino Valenti

Publication date: 6 January 2004

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1007-5704(03)00016-9

zbMATH Keywords

nonlinear wave equationdifferential invariantequivalence group

Mathematics Subject Classification ID

Transformation groups and semigroups (topological aspects) (54H15) Second-order nonlinear hyperbolic equations (35L70) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (10)

Reduction of systems of two nonlinear parabolic type partial differential equations to solvable forms using differential invariants ⋮ Differential invariants of the one-dimensional quasi-linear second-order evolution equation ⋮ On the invariants of two dimensional linear parabolic equations ⋮ Differential invariants for quasi-linear and semi-linear wave-type equations ⋮ On linearization of hyperbolic equations using differential invariants ⋮ Invariants of two- and three-dimensional hyperbolic equations ⋮ Benjamin-Bona-Mahony (BBM) equation with variable coefficients: similarity reductions and Painlevé analysis ⋮ Differential invariants for third-order evolution equations ⋮ Differential invariants for systems of linear hyperbolic equations ⋮ Complete group classification of a class of nonlinear wave equations

Cites Work

• Symmetry classification and optimal systems of a non-linear wave equation
• Group properties and invariant solutions for infinitesimal transformations of a non-linear wave equation
• Group properties of u//(tt)=[f(u)u//x//x]
• Contact transformation group classification of nonlinear wave equations
• On a countable-dimensional subalgebra of the equivalence algebra for equations v tt=f(x,v x)v xx+g(x,v x)
• Preliminary group classification of equations v t t=f (x,v x)v x x+g(x,v x)
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