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...

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

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...

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...

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

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...

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

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

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...

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

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

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

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

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

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

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

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

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...

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

the superposition principle holds (which is often but not always; see nonlinear optics), the behavior of any light wave can be understood as a superposition...

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...

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...

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...

equation Vlasov equation Dirac equation, the relativistic wave equation for electrons and positrons Gardner equation Klein–Gordon equation Knizhnik–Zamolodchikov...