Stationary states of the nonlinear Dirac equation: A variational approach
From MaRDI portal
Publication:1907984
DOI10.1007/BF02099273zbMath0843.35114OpenAlexW2019177003MaRDI QIDQ1907984
Publication date: 15 February 1996
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02099273
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55)
Related Items
Nonrelativistic Asymptotics of Solitary Waves in the Dirac Equation with Soler-Type Nonlinearity, Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential, Localized solutions of the Dirac–Maxwell equations, Error analysis of a time fourth-order exponential wave integrator Fourier pseudo-spectral method for the nonlinear Dirac equation, Symmetric solutions for a 2D critical Dirac equation, Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations, Existence and asymptotic behaviour of the least energy solutions for a quasilinear Dirac-Poisson system, Relative Morse index and multiple solutions for a non-periodic Dirac equation with external fields, Existence of semiclassical solutions for some critical Dirac equation, Existence and concentration of semi-classical solutions for a nonlinear Maxwell-Dirac system, Ground state solutions for nonperiodic Dirac equation with superquadratic nonlinearity, Unnamed Item, From atoms to crystals: a mathematical journey, Infinitely many large energy solutions for superlinear Dirac equations, Soliton dynamics in the ABS nonlinear spinor model with external fields, High-order conservative schemes for the nonlinear Dirac equation, Stationary state computation for nonlinear Dirac operators, On the continuum limit for a model of binary waveguide arrays, The nonlinear Dirac equation in Bose-Einstein condensates: foundation and symmetries, Unnamed Item, Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field, A spherically symmetric bound state of the coupled Maxwell-Dirac equations with self-interaction alone, On Stability of Standing Waves of Nonlinear Dirac Equations, On multiplicity of semi-classical solutions to a nonlinear Maxwell-Dirac system, Solitary waves for nonlinear Klein-Gordon equations coupled with Born-Infeld theory, A boundary value problem for the nonlinear Dirac equation on compact spin manifold, Multiplicity and concentration of semi-classical solutions to nonlinear Dirac-Klein-Gordon systems, Existence of ground state solutions to Dirac equations with vanishing potentials at infinity, Analysis of models for quantum transport of electrons in graphene layers, Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime, Numerical methods for nonlinear Dirac equation, Clifford algebra, Lorentz transformation and unified field theory, Curvature effect in the spinorial Yamabe problem on product manifolds, Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations, Bifurcation solutions for a nonlinear Dirac equation, Semiclassical states for Dirac-Klein-Gordon system with critical growth, Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity, Morse-Floer theory for superquadratic Dirac equations. I: Relative Morse indices and compactness, Bound-state solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems, Solutions of super linear Dirac equations with general potentials, Morse homology for asymptotically linear Dirac equations on compact manifolds, Ground states for Dirac equation with singular potential and asymptotically periodic condition, Morse-Floer theory for superquadratic Dirac-geodesics, Periodic waves of nonlinear Dirac equations, Semiclassical limits of ground states for Hamiltonian elliptic system with gradient term, On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system, Unnamed Item, Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory, Semi-classical limits of ground states of a nonlinear Dirac equation, Concentration behavior of semiclassical solutions for Hamiltonian elliptic system, On a class of infinite-dimensional Hamiltonian systems with asymptotically periodic nonlinearities, Existence and concentration of semiclassical solutions for Hamiltonian elliptic system, Existence results for solutions to nonlinear Dirac equations on compact spin manifolds, Virial identities and energy-momentum relation for solitary waves of nonlinear Dirac equations, On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system, Lax pair and new exact solutions of the nonlinear Dirac equation, The Dirac–Maxwell equations with cylindrical symmetry, Unnamed Item, Variational methods in relativistic quantum mechanics, Multiple solutions for a class of nonperiodic Dirac equations with vector potentials, Homoclinic orbits for an unbounded superquadratic Hamiltonian systems, On nonlinear Dirac equations, Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit, Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation, Strongly localized semiclassical states for nonlinear Dirac equations, Admissible solutions for Dirac equations with singular and non-monotone nonlinearity, Existence and multiplicity of stationary solutions for a class of Maxwell-Dirac system, ON SEMICLASSICAL GROUND STATES OF A NONLINEAR DIRAC EQUATION, Existence of Hartree-Fock excited states for atoms and molecules, Existence and exponential decay of ground-state solutions for a nonlinear Dirac equation, An infinite sequence of localized semiclassical bound states for nonlinear Dirac equations, Periodic solutions of an asymptotically linear Dirac equation, Solutions of Dirac equations on compact spin manifolds via saddle point reduction, Chaos, solitons and fractals in the nonlinear Dirac equation, A strongly degenerate elliptic equation arising from the semilinear Maxwell equations, Semiclassical states of nonlinear Dirac equations with degenerate potential, Towards a unified field theory for classical electrodynamics, Solutions of non-periodic super-quadratic Dirac equations, Periodic solutions of a Dirac equation with concave and convex nonlinearities, Solutions of nonlinear Dirac equations, A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent, Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation, Infinitely many solutions of Dirac equations with concave and convex nonlinearities, STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS, On semiclassical states for Dirac equations, Weakly localized states for nonlinear Dirac equations, On multiplicity of semi-classical solutions to nonlinear Dirac equations of space-dimension \(n\), On the concentration of semiclassical states for nonlinear Dirac equations, Solutions of a nonlinear Dirac equation with external fields, Stationary solutions for a superlinear Dirac equation, Infinitely many solutions for a class of nonlinear Dirac equations without symmetry, On spectral stability of the nonlinear Dirac equation, Ground states for nonlinear Maxwell-Dirac system with magnetic field, On linear instability of solitary waves for the nonlinear Dirac equation, Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations, Semiclassical states for nonlinear Dirac equations with singular potentials, Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system, The nonlinear Dirac equation in Bose–Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices, Ground state homoclinic orbits for first-order Hamiltonian system, Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation, Nontrivial solution of a semilinear schrödinger equation, The concentration behavior of ground state solutions for nonlinear Dirac equation, An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity, On the multiple existence of superquadratic Dirac-harmonic maps into flat tori, Some properties of the spinor soliton, Existence and decay property of ground state solutions for Hamiltonian elliptic system, Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential, Semiclassical states for coupled nonlinear Schrödinger system with competing potentials, Solutions of a class of Hamiltonian elliptic systems in \(\mathbb R^N\), An index theory with applications to homoclinic orbits of Hamiltonian systems and Dirac equations, Infinitely many localized semiclassical states for critical nonlinear Dirac equations, The solutions of critical nonlinear Dirac equations with degenerate potential, Localized concentration of semi-classical states for nonlinear Dirac equations, Periodic solutions of superlinear Dirac equations with perturbations from symmetry, \(L^2\)-normalized solitary wave solutions of a nonlinear Dirac equation
Cites Work
- Unnamed Item
- Nonlinear scalar field equations. I: Existence of a ground state
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- Existence of stationary states for nonlinear Dirac equations
- Existence of excited states for a nonlinear Dirac field
- First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems
- Existence of localized solutions for a classical nonlinear Dirac field
- Periodic solutions of Hamiltonian systems with superquadratic potential
- Critical point theorems for indefinite functionals
- Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits
- Existence of solitary waves in higher dimensions
- Dual variational methods in critical point theory and applications
- Existence of standing waves for Dirac fields with singular nonlinearities
- An Infinite Dimensional Version of Sard's Theorem
- Nonlinear Spinor Fields
