Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2019, Volume 349, pp. 17 - 44

This paper puts forth a high-order weighted essentially non-oscillatory (WENO) finite-difference scheme to numerically generate the viscosity solution of a new class of Hamilton–Jacobi (HJ...

Porous elastomers | Flux numerical methods | Electromagnetic solids | Exact Hamilton–Jacobi solutions | High-order WENO schemes | ELECTROELASTIC DEFORMATIONS | VISCOSITY SOLUTIONS | EFFICIENT IMPLEMENTATION | CAVITATION | CLOSED-FORM SOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | DIELECTRIC ELASTOMER COMPOSITES | Exact Hamilton-Jacobi solutions | HOMOGENIZATION | ORDER | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Electromagnetism | Magnetic fields | Electric fields | Analysis | Elastomers | Solid mechanics | Viscosity | Nonlinear equations | Deformation | Particulate composites | Inclusions | Free energy | Domains | Composite materials | Ferrofluids | Runge-Kutta method | Mathematical models | Hamiltonian functions | Finite difference method

Porous elastomers | Flux numerical methods | Electromagnetic solids | Exact Hamilton–Jacobi solutions | High-order WENO schemes | ELECTROELASTIC DEFORMATIONS | VISCOSITY SOLUTIONS | EFFICIENT IMPLEMENTATION | CAVITATION | CLOSED-FORM SOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | DIELECTRIC ELASTOMER COMPOSITES | Exact Hamilton-Jacobi solutions | HOMOGENIZATION | ORDER | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Electromagnetism | Magnetic fields | Electric fields | Analysis | Elastomers | Solid mechanics | Viscosity | Nonlinear equations | Deformation | Particulate composites | Inclusions | Free energy | Domains | Composite materials | Ferrofluids | Runge-Kutta method | Mathematical models | Hamiltonian functions | Finite difference method

Journal Article

Indian Journal of Physics, ISSN 0973-1458, 5/2017, Volume 91, Issue 5, pp. 521 - 526

We investigate the exact solutions of the Dirac equation for Makarov potential under the condition of equal vector and scalar potentials in the context of the quantum Hamilton–Jacobi formalism...

Quantum Hamilton–Jacobi formalism | Astrophysics and Astroparticles | Dirac equation | Makarov potential | Quantum momentum function | Physics, general | Energy eigenfunctions | Physics | MECHANICS | PHYSICS, MULTIDISCIPLINARY | Quantum Hamilton-Jacobi formalism | Energy | Quantum physics | Mathematical analysis | Exact solutions | Scalars | Polynomials | Wave functions | Formalism

Quantum Hamilton–Jacobi formalism | Astrophysics and Astroparticles | Dirac equation | Makarov potential | Quantum momentum function | Physics, general | Energy eigenfunctions | Physics | MECHANICS | PHYSICS, MULTIDISCIPLINARY | Quantum Hamilton-Jacobi formalism | Energy | Quantum physics | Mathematical analysis | Exact solutions | Scalars | Polynomials | Wave functions | Formalism

Journal Article

International journal of theoretical physics, ISSN 1572-9575, 2012, Volume 51, Issue 8, pp. 2427 - 2432

In this letter we investigate the separability of the Klein–Gordon and Hamilton–Jacobi equation in Gödel universe...

Integrability | Theoretical, Mathematical and Computational Physics | Exact solutions | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Gödel universe | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | METRICS | GEODESICS | Godel universe

Integrability | Theoretical, Mathematical and Computational Physics | Exact solutions | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Gödel universe | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | METRICS | GEODESICS | Godel universe

Journal Article

Annals of Physics, ISSN 0003-4916, 2005, Volume 320, Issue 1, pp. 164 - 174

We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton–Jacobi approach...

Band spectra | Scarf potential | Quantum Hamilton–Jacobi formalism | Bound state spectra | 03.65. Ca | 03.65. Ge | Quantum Hamilton-Jacobi formalism | MECHANICS | quantum Hamilton-Jacobi formalism | scarf potential | PHYSICS, MULTIDISCIPLINARY | bound state spectra | EQUATION | band spectra | Physics - Quantum Physics | EIGENVALUES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | SINGULARITY | EXACT SOLUTIONS | HAMILTON-JACOBI EQUATIONS | EIGENFUNCTIONS | POTENTIALS | PERIODICITY | BOUND STATE | BOUNDARY CONDITIONS

Band spectra | Scarf potential | Quantum Hamilton–Jacobi formalism | Bound state spectra | 03.65. Ca | 03.65. Ge | Quantum Hamilton-Jacobi formalism | MECHANICS | quantum Hamilton-Jacobi formalism | scarf potential | PHYSICS, MULTIDISCIPLINARY | bound state spectra | EQUATION | band spectra | Physics - Quantum Physics | EIGENVALUES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | SINGULARITY | EXACT SOLUTIONS | HAMILTON-JACOBI EQUATIONS | EIGENFUNCTIONS | POTENTIALS | PERIODICITY | BOUND STATE | BOUNDARY CONDITIONS

Journal Article

Applied mathematical modelling, ISSN 0307-904X, 2012, Volume 36, Issue 11, pp. 5614 - 5623

In this paper, we give an analytical-approximate solution for the Hamilton–Jacobi–Bellman (HJB) equation arising in optimal control problems using...

Hamilton–Jacobi–Bellman equation | Homotopy perturbation method | Optimal control problems | He’s polynomials | Hamilton-Jacobi-Bellman equation | He's polynomials | VARIATIONAL ITERATION METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DECOMPOSITION METHOD | Approximation | Perturbation methods | Mathematical analysis | Optimal control | Exact solutions | Mathematical models | Models | Modelling

Hamilton–Jacobi–Bellman equation | Homotopy perturbation method | Optimal control problems | He’s polynomials | Hamilton-Jacobi-Bellman equation | He's polynomials | VARIATIONAL ITERATION METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DECOMPOSITION METHOD | Approximation | Perturbation methods | Mathematical analysis | Optimal control | Exact solutions | Mathematical models | Models | Modelling

Journal Article

The Bulletin of Irkutsk State University. Series Mathematics, ISSN 1997-7670, 2019, Volume 28, Issue 1, pp. 53 - 68

.... Such type of Hamilton-Jacobi like equations are considered in mechanics and control theory...

Hamilton-Jacobi type equations | exact solutions | nonlinear system

Hamilton-Jacobi type equations | exact solutions | nonlinear system

Journal Article

Journal of mathematics in industry, ISSN 2190-5983, 2019, Volume 9, Issue 1, pp. 1 - 26

We formulate a stochastic impulse control model for animal population management and a candidate of exact solutions to a Hamilton–Jacobi...

Viscosity | Performance indices | Numerical methods | Exact solutions | Animal populations | Portfolio management | Inequality | Threshold control | Hamilton–Jacobi–Bellman quasi-variational inequalities | Population management | Feeding damage | Uniqueness and existence of solution | Viscosity solution

Viscosity | Performance indices | Numerical methods | Exact solutions | Animal populations | Portfolio management | Inequality | Threshold control | Hamilton–Jacobi–Bellman quasi-variational inequalities | Population management | Feeding damage | Uniqueness and existence of solution | Viscosity solution

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 2/2016, Volume 168, Issue 2, pp. 699 - 722

.... An extended Hamilton–Jacobi–Bellman equation system and a verification theorem are provided to derive the equilibrium strategy and the equilibrium value function...

Hamilton–Jacobi–Bellman equation | 60H20 | Equilibrium strategy | Non-exponential discount function | Mathematics | Theory of Computation | Optimization | Dual model | 93E20 | 91A10 | Dividend payment | 91G10 | Calculus of Variations and Optimal Control; Optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | MATHEMATICS, APPLIED | PAYMENTS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Hamilton-Jacobi-Bellman equation | DIFFUSION-PROCESSES | POLICIES | RUIN | Dividends | Models | Studies | Partial differential equations | Equilibrium | Game theory | Illustrations | Mathematical analysis | Exact solutions | Strategy | Discounts | Mathematical models | Program verification (computers)

Hamilton–Jacobi–Bellman equation | 60H20 | Equilibrium strategy | Non-exponential discount function | Mathematics | Theory of Computation | Optimization | Dual model | 93E20 | 91A10 | Dividend payment | 91G10 | Calculus of Variations and Optimal Control; Optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | MATHEMATICS, APPLIED | PAYMENTS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Hamilton-Jacobi-Bellman equation | DIFFUSION-PROCESSES | POLICIES | RUIN | Dividends | Models | Studies | Partial differential equations | Equilibrium | Game theory | Illustrations | Mathematical analysis | Exact solutions | Strategy | Discounts | Mathematical models | Program verification (computers)

Journal Article

Optimal Control Applications and Methods, ISSN 0143-2087, 03/2017, Volume 38, Issue 2, pp. 229 - 246

.... Based on the technique of stochastic control theory and the corresponding extended Hamilton...

Hamilton–Jacobi–Bellman equation | portfolio | mean‐variance utility | jump‐diffusion process | common shock | time‐consistent strategy | state dependent risk aversion | time-consistent strategy | jump-diffusion process | mean-variance utility | MATHEMATICS, APPLIED | POISSON | TIME | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Hamilton-Jacobi-Bellman equation | SELECTION | LIABILITY MANAGEMENT | AUTOMATION & CONTROL SYSTEMS | Investment analysis | Game theory | Mathematical analysis | Optimal control | Exact solutions | Risk | Strategy | Mathematical models | Terminals | Optimization

Hamilton–Jacobi–Bellman equation | portfolio | mean‐variance utility | jump‐diffusion process | common shock | time‐consistent strategy | state dependent risk aversion | time-consistent strategy | jump-diffusion process | mean-variance utility | MATHEMATICS, APPLIED | POISSON | TIME | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Hamilton-Jacobi-Bellman equation | SELECTION | LIABILITY MANAGEMENT | AUTOMATION & CONTROL SYSTEMS | Investment analysis | Game theory | Mathematical analysis | Optimal control | Exact solutions | Risk | Strategy | Mathematical models | Terminals | Optimization

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 06/2017, Volume 34, Issue 14, p. 145009

... a coupled system of general relativity and a scalar field in the Hamilton-Jacobi formalism. This suggests the existence of a 'mother' tensor model which derives CTM...

Hamilton-Jacobi | exact solutions | canonical tensor model | constraints | quantization | quantisation | TRIANGLE-HINGE MODELS | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | NETWORKS | GRAVITY | PHYSICS, PARTICLES & FIELDS

Hamilton-Jacobi | exact solutions | canonical tensor model | constraints | quantization | quantisation | TRIANGLE-HINGE MODELS | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | NETWORKS | GRAVITY | PHYSICS, PARTICLES & FIELDS

Journal Article

Automatica, ISSN 0005-1098, 2012, Volume 48, Issue 1, pp. 95 - 101

.... The MUSL can be characterized using optimal control techniques. This variational approach leads to a Hamilton–Jacobi...

Hamilton–Jacobi–Bellman equation | Stability analysis | Worst-case switching law | Barabanov norm | First integral | Positive linear switched system | HamiltonJacobiBellman equation | JOINT SPECTRAL-RADIUS | COUNTEREXAMPLE | ENGINEERING, ELECTRICAL & ELECTRONIC | Hamilton-Jacobi-Bellman equation | FAMILIES | COMPUTATION | AUTOMATION & CONTROL SYSTEMS | POLYTOPE NORMS | Parallelograms | Origins | Law | Mathematical analysis | Exact solutions | Norms | Mathematical models | Switching

Hamilton–Jacobi–Bellman equation | Stability analysis | Worst-case switching law | Barabanov norm | First integral | Positive linear switched system | HamiltonJacobiBellman equation | JOINT SPECTRAL-RADIUS | COUNTEREXAMPLE | ENGINEERING, ELECTRICAL & ELECTRONIC | Hamilton-Jacobi-Bellman equation | FAMILIES | COMPUTATION | AUTOMATION & CONTROL SYSTEMS | POLYTOPE NORMS | Parallelograms | Origins | Law | Mathematical analysis | Exact solutions | Norms | Mathematical models | Switching

Journal Article

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, ISSN 0022-0434, 2013, Volume 135, Issue 4

.... The results reveal that the proposed methods are very effective and simple. Comparisons are made between the results of two proposed methods and the exact solutions.

Hamilton-Jacobi- Bellman equation | Optimal control problems | Differential transform method | optimal control problems | INSTRUMENTS & INSTRUMENTATION | Hamilton-Jacobi-Bellman equation | differential transform method | EQUATIONS | ADOMIAN DECOMPOSITION METHOD | AUTOMATION & CONTROL SYSTEMS | Control theory | Research | Dynamic programming | Invariants | Differential equations | Dynamics | Mathematical analysis | Optimal control | Transforms | Exact solutions | Maximum principle | Dynamical systems | Optimization

Hamilton-Jacobi- Bellman equation | Optimal control problems | Differential transform method | optimal control problems | INSTRUMENTS & INSTRUMENTATION | Hamilton-Jacobi-Bellman equation | differential transform method | EQUATIONS | ADOMIAN DECOMPOSITION METHOD | AUTOMATION & CONTROL SYSTEMS | Control theory | Research | Dynamic programming | Invariants | Differential equations | Dynamics | Mathematical analysis | Optimal control | Transforms | Exact solutions | Maximum principle | Dynamical systems | Optimization

Journal Article

Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, 08/2012, Volume 2012, Issue 8, pp. 18 - 18

.... We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor...

Particle physics - cosmology connection | Physics of the early universe | Inflation | UNIVERSE SCENARIO | FIELD | PROBE WMAP OBSERVATIONS | inflation | K-ESSENCE | particle physics - cosmology connection | COSMOLOGICAL MODELS | FLUCTUATIONS | ASTRONOMY & ASTROPHYSICS | DYNAMICS | QUINTESSENTIAL INFLATION | BRANEWORLD INFLATION | physics of the early univers | UNIFIED DARK-MATTER | PHYSICS, PARTICLES & FIELDS | Tensors | Chaos theory | Mathematical analysis | Cosmic microwave background | Exact solutions | Scalars | Mathematical models | Spectra | TENSORS | HAMILTON-JACOBI EQUATIONS | INFLATONS | POTENTIALS | INFLATIONARY UNIVERSE | CHAOS THEORY | ATTRACTORS | MATHEMATICAL SOLUTIONS | COSMOLOGY | NONLUMINOUS MATTER | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | SCALAR FIELDS | ASTROPHYSICS | RELICT RADIATION

Particle physics - cosmology connection | Physics of the early universe | Inflation | UNIVERSE SCENARIO | FIELD | PROBE WMAP OBSERVATIONS | inflation | K-ESSENCE | particle physics - cosmology connection | COSMOLOGICAL MODELS | FLUCTUATIONS | ASTRONOMY & ASTROPHYSICS | DYNAMICS | QUINTESSENTIAL INFLATION | BRANEWORLD INFLATION | physics of the early univers | UNIFIED DARK-MATTER | PHYSICS, PARTICLES & FIELDS | Tensors | Chaos theory | Mathematical analysis | Cosmic microwave background | Exact solutions | Scalars | Mathematical models | Spectra | TENSORS | HAMILTON-JACOBI EQUATIONS | INFLATONS | POTENTIALS | INFLATIONARY UNIVERSE | CHAOS THEORY | ATTRACTORS | MATHEMATICAL SOLUTIONS | COSMOLOGY | NONLUMINOUS MATTER | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | SCALAR FIELDS | ASTROPHYSICS | RELICT RADIATION

Journal Article

Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2016, Volume 2016, Issue 29, pp. 1 - 16

In this paper, by Karamata regular variation theory and the method of lower and upper solutions, we give an exact boundary behavior for the unique solution near...

Lower and upper solutions | Singular Dirichlet problem | Infinity-Laplacian | The exact asymptotic behavior | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | HAMILTON-JACOBI EQUATIONS | TERM | the exact asymptotic behavior | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | lower and upper solutions | singular Dirichlet problem | infinity-Laplacian | ELLIPTIC-EQUATIONS | ABSORPTION | BLOW-UP SOLUTIONS | UNIQUE POSITIVE SOLUTION | singular dirichlet problem | infinity-laplacian

Lower and upper solutions | Singular Dirichlet problem | Infinity-Laplacian | The exact asymptotic behavior | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | HAMILTON-JACOBI EQUATIONS | TERM | the exact asymptotic behavior | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | lower and upper solutions | singular Dirichlet problem | infinity-Laplacian | ELLIPTIC-EQUATIONS | ABSORPTION | BLOW-UP SOLUTIONS | UNIQUE POSITIVE SOLUTION | singular dirichlet problem | infinity-laplacian

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2009, Volume 14, Issue 5, pp. 1958 - 1961

.... New exact analytical solutions for the quantum Hamilton–Jacobi equation have been obtained for the quantum generating function of quantum theory for the first time...

Exact analytical solution | The quantum generating function | The quantum Hamilton–Jacobi equation | The quantum Hamilton-Jacobi equation | MATHEMATICS, APPLIED | MECHANICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Quantum theory | Nonlinearity | Mathematical models | Hamilton-Jacobi equation | Computer simulation | Mathematical analysis

Exact analytical solution | The quantum generating function | The quantum Hamilton–Jacobi equation | The quantum Hamilton-Jacobi equation | MATHEMATICS, APPLIED | MECHANICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Quantum theory | Nonlinearity | Mathematical models | Hamilton-Jacobi equation | Computer simulation | Mathematical analysis

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2020, Volume 269, Issue 7, pp. 5730 - 5753

We investigated several global behaviors of the weak KAM solutions uc(x,t) parametrized by c∈H1(T,R). For the suspended Hamiltonian H...

Exact syplectic twist map | Aubry Mather theory | Hamilton Jacobi equation | Generalized characteristics | Transition chain | Weak KAM solution

Exact syplectic twist map | Aubry Mather theory | Hamilton Jacobi equation | Generalized characteristics | Transition chain | Weak KAM solution

Journal Article

Journal of Applied Mechanics, Transactions ASME, ISSN 0021-8936, 02/2015, Volume 82, Issue 2, pp. np - np

... (ISP) (Airy's precession). Based on the Hamilton-Jacobi formalism and using the techniques of variation of parameters along with the averaging method, we obtain approximate analytical solutions, in terms of which the...

apsidal precession | variation of parameters | averaging method | Hamilton-Jacobi formalism | ideal spherical pendulum | physical symmetrical pendulum | MECHANICS | PLANE | SPHERICAL PENDULUM | Precession | Approximation | Asymmetry | Mathematical analysis | Pendulums | Exact solutions | Mathematical models | Formalism | Standards | Physics - Classical Physics

apsidal precession | variation of parameters | averaging method | Hamilton-Jacobi formalism | ideal spherical pendulum | physical symmetrical pendulum | MECHANICS | PLANE | SPHERICAL PENDULUM | Precession | Approximation | Asymmetry | Mathematical analysis | Pendulums | Exact solutions | Mathematical models | Formalism | Standards | Physics - Classical Physics

Journal Article

Physical Review A, ISSN 2469-9926, 05/2018, Volume 97, Issue 5

We make use of the quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields...

MECHANICS | STATES | ALIGNMENT | SPECTROSCOPY | ORIENTATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | NONRESONANT LASER FIELDS | OPTICS | ORIENTED MOLECULES | QUASI-EXACT SOLVABILITY | PENDULAR MOLECULES

MECHANICS | STATES | ALIGNMENT | SPECTROSCOPY | ORIENTATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | NONRESONANT LASER FIELDS | OPTICS | ORIENTED MOLECULES | QUASI-EXACT SOLVABILITY | PENDULAR MOLECULES

Journal Article

19.
Full Text
The exact asymptotic behavior of blow-up solutions to a highly degenerate elliptic problem

Boundary Value Problems, ISSN 1687-2762, 12/2015, Volume 2015, Issue 1, pp. 1 - 12

In this paper, by constructing new comparison functions, we mainly study the boundary behavior of solutions to boundary blow-up elliptic problems for more general nonlinearities f...

highly degenerate elliptic equations | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | blow-up solutions | the exact asymptotic behavior | Partial Differential Equations | comparison functions | BOUNDARY SOLUTION | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | HAMILTON-JACOBI EQUATIONS | UNIQUENESS | MATHEMATICS | INFINITY-LAPLACIAN | EXPANSION | Theorems (Mathematics) | Boundary value problems | Usage | Series, Dirichlet | Tests, problems and exercises | Infinity | Asymptotic properties | Mathematical analysis | Smooth boundaries | Texts | Nonlinearity | Boundaries

highly degenerate elliptic equations | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | blow-up solutions | the exact asymptotic behavior | Partial Differential Equations | comparison functions | BOUNDARY SOLUTION | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | HAMILTON-JACOBI EQUATIONS | UNIQUENESS | MATHEMATICS | INFINITY-LAPLACIAN | EXPANSION | Theorems (Mathematics) | Boundary value problems | Usage | Series, Dirichlet | Tests, problems and exercises | Infinity | Asymptotic properties | Mathematical analysis | Smooth boundaries | Texts | Nonlinearity | Boundaries

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2012, Volume 53, Issue 10, p. 103516

.... In our approach, at lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof...

SPACE | GAUGE-THEORIES | PHYSICS, MATHEMATICAL | GEOMETRY | Mathematical analysis | Exact solutions | Eigenvalues | Oscillations | Nonlinearity | Mathematical models | Schroedinger equation | Oscillators | EXCITED STATES | YANG-MILLS THEORY | TRANSPORT THEORY | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | ANHARMONIC OSCILLATORS | EXACT SOLUTIONS | MINKOWSKI SPACE | HAMILTON-JACOBI EQUATIONS | EIGENFUNCTIONS | WAVE FUNCTIONS | EIGENVALUES | NONLINEAR PROBLEMS | SPACE-TIME | PERTURBATION THEORY | HARMONIC OSCILLATORS | OSCILLATIONS | BANACH SPACE | COERCIVE FORCE | GROUND STATES

SPACE | GAUGE-THEORIES | PHYSICS, MATHEMATICAL | GEOMETRY | Mathematical analysis | Exact solutions | Eigenvalues | Oscillations | Nonlinearity | Mathematical models | Schroedinger equation | Oscillators | EXCITED STATES | YANG-MILLS THEORY | TRANSPORT THEORY | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | ANHARMONIC OSCILLATORS | EXACT SOLUTIONS | MINKOWSKI SPACE | HAMILTON-JACOBI EQUATIONS | EIGENFUNCTIONS | WAVE FUNCTIONS | EIGENVALUES | NONLINEAR PROBLEMS | SPACE-TIME | PERTURBATION THEORY | HARMONIC OSCILLATORS | OSCILLATIONS | BANACH SPACE | COERCIVE FORCE | GROUND STATES

Journal Article

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