A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals

@article{Jamal2019ASO,
  title={A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals},
  author={Sameerah Jamal},
  journal={International Journal of Geometric Methods in Modern Physics},
  year={2019}
}
  • S. Jamal
  • Published 16 January 2019
  • Mathematics
  • International Journal of Geometric Methods in Modern Physics
The investigation of approximate symmetries of reparametrization invariant Lagrangians of [Formula: see text] degrees of freedom and quadratic velocities is presented. We show that extra conditions emerge which give rise to approximate and conditional Noether symmetries of such constrained actions. The Noether symmetries are the simultaneous conformal Killing vectors of both the kinetic metric and the potential. In order to recover these conditional symmetry generators which would otherwise be… 
Dynamical systems: Approximate Lagrangians and Noether symmetries
  • S. Jamal
  • Mathematics
    International Journal of Geometric Methods in Modern Physics
  • 2019
We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In
Constrained dynamics: generalized Lie symmetries, singular Lagrangians, and the passage to Hamiltonian mechanics
Guided by the symmetries of the Euler–Lagrange equations of motion, a study of the constrained dynamics of singular Lagrangians is presented. We find that these equations of motion admit a
Lie symmetries and singularity analysis for generalized shallow-water equations
Abstract We perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm (CH) equation and the generalized
Approximate symmetries and similarity solutions for wave equations on liquid films
We study the exact and approximate Lie symmetries for two equations which describe long waves with small amplitude on liquid films. Specifically, we study the 1+2 Benney-Luke and the 1+1 Benney-Lin
Moving front solutions of a time-fractional power-law fluid under gravity
Abstract This paper considers a fractional-order, incompressible power-law fluid on a horizontal plane, where the time component is defined by Riemann-Liouville derivatives. The model is
Imaging Noise Suppression: Fourth-Order Partial Differential Equations and Travelling Wave Solutions
In this paper, we discuss travelling wave solutions for image smoothing based on a fourth-order partial differential equation. One of the recurring issues of digital imaging is the amount of noise.

References

SHOWING 1-10 OF 20 REFERENCES
Lie point and variational symmetries in minisuperspace Einstein gravity
We consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrization invariant Lagrangians quadratic in the velocities; such Lagrangians
nth-Order Approximate Lagrangians Induced by Perturbative Geometries
  • S. Jamal
  • Mathematics
    Mathematical Physics, Analysis and Geometry
  • 2018
A family of perturbative Lagrangians that describe approximate and multidimensional Klein-Gordon equations are studied. We probe the existence of approximate Noether symmetries via generalized
The geometric nature of approximate Noether gauge symmetries
We find the geometrical set of equations corresponding to the approximate Noether gauge symmetry conditions of the perturbed geodesic Lagrangian for spacetimes. Using the obtained new set of
Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The
Conditional symmetries in parametrized field theories
In parametrized field theories, spacelike hypersurfaces and fields which they carry are evolved by a Hamiltonian which is a linear combination of the super‐Hamiltonian and supermomentum constraints.
Invariant solutions and Noether symmetries in Hybrid Gravity
Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific
Approximate conditions admitted by classes of the Lagrangian L=12(-u′2+u2)+ϵiGi(u, u′, u″)
Symmetry, Singularities and Integrability in Complex Dynamics III: Approximate Symmetries and Invariants
Abstract The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations
...
...