Approximate nonlinear self-adjointness and approximate conservation laws

DOI10.1088/1751-8113/46/15/155203zbMath1267.81155arXiv1301.4534OpenAlexW2951444615MaRDI QIDQ4921794

Zhi Yong Zhang

Publication date: 13 May 2013

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.6694

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) NLS equations (nonlinear Schrödinger equations) (35Q55) Nonlinear higher-order PDEs (35G20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

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Nonlinear and linearised primal and dual initial boundary value problems: when are they bounded? How are they connected? ⋮ Adjoint symmetry and conservation law of nonlinear diffusion equations with convection and source terms ⋮ Conservation laws of partial differential equations: symmetry, adjoint symmetry and nonlinear self-adjointness ⋮ First order approximate conserved quantities induced by the approximate symmetries of the perturbed Lagrangian ⋮ Nonlinear self-adjointness of a class of third order nonlinear dispersive equations ⋮ Nonlinear self-adjoint classification of a Burgers-KdV family of equations ⋮ On the existence of conservation law multiplier for partial differential equations ⋮ Approximate conditions admitted by classes of the Lagrangian \(\mathcal{L} = \frac{1}{2}(- u^{\prime 2} + u^2) + \epsilon^i g_i(u, u^\prime, u)\) ⋮ Group analysis and nonlinear self-adjointness for a generalized breaking soliton equation

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