The Gardner equation is an
integrable nonlinear partial differential equation
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear system, nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have b ...
introduced by the mathematician
Clifford Gardner in 1968 to generalize
KdV equation and
modified KdV equation. The Gardner equation has applications in
hydrodynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...
,
plasma physics
Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including th ...
and
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
:
where
is an arbitrary real parameter.
See also
*
Korteweg–de Vries equation
Notes
References
*
Nonlinear partial differential equations
Integrable systems
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