Results 1 to 10 of about 4,585 (80)

Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction [PDF]

, 2004
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions.
Abraham, Cartier, Cartier, Cartier, Dunkl, Duru, Dynkin, Elworthy, Feynman, Freidlin, Friedman, Glimm, Grosche, J. LaChapelle, Lachapelle, Sagan, Young   +16 more
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Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces [PDF]

, 1997
We use so-called energy-dependent Schrödinger operators to establish a link between special classes of solutions on N-component systems of evolution equations and finite dimensional Hamiltonian systems on the moduli spaces of Riemann surfaces.
Alber, Mark S., Luther, Gregory G., Marsden, Jerrold E.   +2 more
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Steve Smale and Geometric Mechanics [PDF]

, 1993
Thus, one can say-perhaps with only a slight danger of oversimplification- that reduction theory synthesises the work of Smale, Arnold (and their predecesors of course) into a bundle, with Smale as the base and Arnold as the fiber.
Marsden, Jerrold E.
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Lagrange Anchor for Bargmann-Wigner equations [PDF]

, 2013
A Poincare invariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin s > 1/2 in four-dimensional Minkowski space.
D Lipkin, DB Fairlie, DS Kaparulin, DS Kaparulin, DS Kaparulin, LA Dickey, MA Vasiliev, MA Vasiliev, MA Vasiliev, R Penrose, S Anco, S Anco, S Anco, SL Lyakhovich, T Morgan, TWB Kibble, Y Kosmann-Schwarzbach   +16 more
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Analytic solutions of the Madelung equation [PDF]

, 2017
We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum ...
Barna, Imre F., Mátyás, László, Pocsai, Mihály A.   +2 more
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Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

, 2020
We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman's functionals and related entropic values are
Bubuianu, Laurenţiu, Vacaru, Sergiu I., Veliev, Elşen Veli   +2 more
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Lie systems: theory, generalisations, and applications [PDF]

, 2011
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the ...
J. De Lucas, J. De Lucas, J. F. Cari ˜nena, J. F. Cariñena   +3 more
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Higher Spin Symmetries and Deformed Schr\"odinger Algebra in Conformal Mechanics

, 2018
The dynamical symmetries of $1+1$-dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial De Alfaro-Fubini-Furlan, DFF, damping term) are investigated.
Toppan, Francesco, Valenzuela, Mauricio
core   +1 more source

On Integrable Doebner-Goldin Equations

, 1995
We suggest a method for integrating sub-families of a family of nonlinear {\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie} symmetries.
Anderson R L, Burgers J M, Cole J D, Courant R, Doebner H-D, Doebner H-D, Doebner H-D, Doebner H-D, Doebner H-D, Feynman R P, Fushchych W I, Fushchych W I, Fushchych W I, Fushchych W I, Fushchych W I, Fushchych W I, Goldin G A, Goldin G A, Guerra F, Hopf E, John F, Kibble T W B, Lax P, Lücke W, Nattermann P, Nattermann P, Nattermann P, Olver P J, Ovsiannikov L V, P Nattermann, R Zhdanov, Sabatier P C, Smolin L, Smoller J   +33 more
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Compatibility, multi-brackets and integrability of systems of PDEs [PDF]

, 2008
We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators.
Kruglikov, Boris, Lychagin, Valentin
core   +2 more sources