the notation. In quantum field theory, the nonlinear Dirac equation is a model of self-interacting Dirac fermions. This model is widely considered in...

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including...

satisfied by stationary localized solutions to a nonlinear Schrödinger equation or nonlinear Klein–Gordon equation. It was obtained by S.I. Pokhozhaev and is...

can approximate the force of the impact by a Dirac delta. In doing so, one not only simplifies the equations, but one also is able to calculate the motion...

particles. Its theoretical relevance is similar to that of the Dirac equation. The equation solutions include a scalar or pseudoscalar field[clarification...

Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world...

called fully nonlinear, and possesses nonlinearities on one or more of the highest-order derivatives. An example is the Monge–Ampère equation, which arises...

Schrödinger–Newton equation, sometimes referred to as the Newton–Schrödinger or Schrödinger–Poisson equation, is a nonlinear modification of the Schrödinger equation with...

solving nonlinear differential equations exactly; those that are known typically depend on the equation having particular symmetries. Nonlinear differential...

the Dirac equation in 1928. It connected special relativity and quantum mechanics and predicted the existence of antimatter. The Dirac equations is one...

of equation (2) to the electron – by various manipulations he factorized the equation into the form and one of these factors is the Dirac equation (see...

specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...

(1993). Dirac structures and integrability of nonlinear evolution equations. Wiley. Gay-Balmaz, François; Yoshimura, Hiroaki (2020). "Dirac structures...

in two dimensions and is called bosonization. Dirac equation Gross–Neveu model Nonlinear Dirac equation Soler model Thirring, W. (1958). "A Soluble Relativistic...

turn introducing Dirac matrices. In a modern context, the Klein–Gordon equation describes spin-less particles, while the Dirac equation describes spin-1/2...

equation Dirac equation in curved spacetime Dirac equation in the algebra of physical space Nonlinear Dirac equation Two-body Dirac equations Dirac fermion...

See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....

extended equation, e.g. the Lieb-Liniger Gross–Pitaevskii equation (sometimes called modified or generalized nonlinear Schrödinger equation). The equation has...

The sine-Gordon equation is a second-order nonlinear partial differential equation for a function φ {\displaystyle \varphi } dependent on two variables...

equations are special because they are nonlinear differential equations with known exact solutions. A notable special case of the Bernoulli equation is...

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different...

Commons has media related to Wave equation. Nonlinear Wave Equations by Stephen Wolfram and Rob Knapp, Nonlinear Wave Equation Explorer by Wolfram Demonstrations...

the Born–Infeld model or the Dirac–Born–Infeld action is a particular example of what is usually known as a nonlinear electrodynamics. It was historically...

field equations include the Klein–Gordon equation for spin-0 particles the Dirac equation for spin-1/2 particles the Bargmann–Wigner equations for particles...

convection–diffusion equation. The equation is a nonlinear integro-differential equation, and the unknown function in the equation is a probability density...

represent the point load as a distribution using the Dirac function. In that case the equation and boundary conditions are E I d 4 w d x 4 = F δ ( x...

to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses...

mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability...

relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of classical physics...

symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Charged...