62 research outputs found

    Conservations Laws for Critical Kohn-Laplace Equations on the Heisenberg Group

    Full text link
    Using the complete group classification of semilinear differential equations on the three-dimensional Heisenberg group carried out in a preceding work, we establish the conservation laws for the critical Kohn-Laplace equations via the Noether's Theorem.Comment: 9 pages, 1 table, submitted for publicatio

    Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation

    Get PDF
    We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on MM are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries.Comment: Paper submitted for publicatio

    The intrinsic geometry determined by the Cauchy problems of the Camassa-Holm equation

    Full text link
    Pseudospherical surfaces determined by Cauchy problems involving the Camassa-Holm equation are considered herein. We study how global solutions influence the corresponding surface, as well as we investigate two sorts of singularities of the metric: the first one is just when the co-frame of dual form is not linearly independent. The second sort of singularity is that arising from solutions blowing up. In particular, it is shown that the metric blows up if and only if the solution breaks in finite time

    New conservation laws for inviscid Burgers equation

    Full text link
    • …
    corecore