Morphing quantum mechanics and fluid dynamics

  title={Morphing quantum mechanics and fluid dynamics},
  author={Thomas L. Curtright and David B. Fairlie},
  journal={Journal of Physics A},
We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger equation. 
Implicit Solutions of PDE's
Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which
Method for generating additive shape-invariant potentials from an Euler equation
In the supersymmetric quantum mechanics formalism, the shape invariance condition provides a sufficient constraint to make a quantum mechanical problem solvable, i.e. we can determine its eigenvalues
Phase space holography with no strings attached
Keywords: phase space, holographic correspondence, hydrodynamics, effective metric We discuss the Wigner function representation from the novel standpoint of establishing a natural holographylike
An analytical solution of Monge differential equation
We present the exact solution to the non linear Monge differential equation lambda(x, t)lambdax(x, t) = lambdat(x, t). It is widely accepted that the Monge equation is equivalent to the ODE d2X/dt2=


Turbulence without pressure
We develop exact field theoretic methods to treat turbulence when the effect of pressure is negligible. We find explicit forms of certain probability distributions, demonstrate that the breakdown of
Noncommuting Gauge Fields as a Lagrange Fluid
Abstract The Lagrange description of an ideal fluid gives rise in a natural way to a gauge potential and a Poisson structure that are classical precursors of analogous noncommuting entities. With
Integrable generalizations of the two-dimensional Born-Infeld equation
The Born-Infeld equation in two dimensions is generalized to higher dimensions. Lorentz invariance is retained, and the resulting system is completely integrable via linearization by Legendre
Extra dimensions and nonlinear equations
Solutions of nonlinear multi-component Euler–Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem.
Velocity and velocity-difference distributions in Burgers turbulence.
We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
Quasi-linear Hyperbolic Equations Conservation Laws Single Conservation Laws The Decay of Solutions as t Tends to Infinity Hyperbolic Systems of Conservation Laws Pairs of Conservation Laws Notes
The Geometric Origin of the Madelung Potential
Madelung's hydrodynamical forms of the Schrodinger equation and the Klein-Gordon equation are presented. The physical nature of the quantum potential is explored. It is demonstrated that the
Multi‐Hamiltonian structure of the Born–Infeld equation
The multi‐Hamiltonian structure, conservation laws, and higher order symmetries for the Born–Infeld equation are exhibited. A new transformation of the Born‐Infeld equation to the equations of a
Quantentheorie in hydrodynamischer Form
ZusammenfassungEs wird gezeigt, daß man die Schrödingersche Gleichung des Einelektronen-problems in die Form der hydrodynamischen Gleichungen transformieren kann.
Self-Dual Vortices in Chern–Simons Hydrodynamics
AbstractThe classical theory of a nonrelativistic charged particle interacting with a U(1) gauge field is reformulated as the Schrödinger wave equation modified by the de Broglie–Bohm nonlinear