Variational formulation of approximate symmetries and conservation laws

DOI10.1023/A:1017561629174zbMath1006.81035MaRDI QIDQ5947387

Abdul Hamid Kara, Andrew Gratien Johnpillai

Publication date: 14 February 2003

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

zbMATH Keywords

approximate Lie symmetry generators of a partial differential equationapproximate Noether symmetries

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20)

Related Items (13)

Generalization of approximate partial Noether approach in phase space ⋮ Approximate conservation laws of nonlinear perturbed heat and wave equations ⋮ Approximate conservation laws of perturbed partial differential equations ⋮ First order approximate conserved quantities induced by the approximate symmetries of the perturbed Lagrangian ⋮ Group analysis, invariance results, exact solutions and conservation laws of the perturbed fractional Boussinesq equation ⋮ Lie group analysis and conservation laws for the time-fractional third order KdV-type equation with a small perturbation parameter ⋮ CONSERVATION LAWS OF SOME NON-VARIATIONAL PERTURBED PDE'S VIA A PARTIAL VARIATIONAL APPROACH ⋮ Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter ⋮ Approximate partial Noether operators and first integrals for cubically coupled nonlinear Duffing oscillators subject to a periodically driven force ⋮ Approximate symmetries, conservation laws and numerical solutions for a class of perturbed linear wave type system ⋮ First integrals and analytical solutions of some dynamical systems ⋮ Approximate partial Noether operators and first integrals for coupled nonlinear oscillators ⋮ Approximate conditions admitted by classes of the Lagrangian \(\mathcal{L} = \frac{1}{2}(- u^{\prime 2} + u^2) + \epsilon^i g_i(u, u^\prime, u)\)

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