# Category: Nonlinear partial differential equations

Bretherton equation
In mathematics, the Bretherton equation is a nonlinear partial differential equation introduced by Francis Bretherton in 1964: with integer and While and denote partial derivatives of the scalar field
Chafee–Infante equation
The Chafee–Infante equation is a nonlinear partial differential equation introduced by and .
Seventh-order Korteweg–De Vries equation
The seventh-order Korteweg–De Vries equation is a nonlinear partial differential equation in 1+1 dimensions related to the KdV equation. It is defined by the formula where and are real variables and i
Unnormalized KdV equation
Unnormalized KdV equation is a nonlinear partial differential equation
Benjamin–Ono equation
In mathematics, the Benjamin–Ono equation is a nonlinear partial integro-differential equation that describes one-dimensional internal waves in deep water.It was introduced by and . The Benjamin–Ono e
Broer–Kaup equations
The Broer–Kaup equations are a set of two coupled nonlinear partial differential equations:
Rosenau–Hyman equation
The Rosenau–Hyman equation or K(n,n) equation is a KdV-like equation having compacton solutions. This nonlinear partial differential equation is of the form The equation is named after Philip Rosenau
Fifth-order Korteweg–De Vries equation
A fifth-order Korteweg–De Vries (KdV) equation is a nonlinear partial differential equation in 1+1 dimensions related to the Korteweg–De Vries equation. Fifth order KdV equations may be used to model
Tzitzeica equation
The Tzitzeica equation is a nonlinear partial differential equation devised by Gheorghe Țițeica in 1907 in the study of differential geometry, describing surfaces of constant affine curvature. The Tzi
Modified KdV–Burgers equation
The modified KdV–Burgers equation is a nonlinear partial differential equation
Gardner equation
The Gardner equation is an integrable nonlinear partial differential equation introduced by the mathematician Clifford Gardner in 1968 to generalize KdV equation and modified KdV equation. The Gardner
Hirota–Satsuma equation
The Hirota–Satsuma equation is a set of three coupled nonlinear partial differential equations: The Hirota–Satsuma equation appeared in the theory of shallow water waves, first discussed by Hirota, Ry
Eckhaus equation
In mathematical physics, the Eckhaus equation – or the Kundu–Eckhaus equation – is a nonlinear partial differential equation within the nonlinear Schrödinger class: The equation was independently intr
Schrödinger–Newton equation
The Schrödinger–Newton equation, sometimes referred to as the Newton–Schrödinger or Schrödinger–Poisson equation, is a nonlinear modification of the Schrödinger equation with a Newtonian gravitational
List of nonlinear partial differential equations
See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations.
Drinfeld–Sokolov–Wilson equation
The Drinfeld–Sokolov–Wilson (DSW) equations are an integrable system of two coupled nonlinear partial differential equations proposed by Vladimir Drinfeld and Vladimir Sokolov, and independently by Ge
Fujita–Storm equation
The Fujita–Storm equation is a nonlinear partial differential equation. It occurs frequently in problems of nonlinear heat and mass transfer, combustion theory and theory of flows in porous media
Gibbons–Tsarev equation
The Gibbons–Tsarev equation is an integrable second order nonlinear partial differential equation. In its simplest form, in two dimensions, it may be written as follows: The equation arises in the the
Dodd–Bullough–Mikhailov equation
The Dodd–Bullough–Mikhailov equation is a nonlinear partial differential equation introduced by Roger Dodd, Robin Bullough, and Alexander Mikhailov. In 2005, mathematician Abdul-Majid Wazwaz combined
Unnormalized modified KdV equation
The unnormalized modified Korteweg–de Vries (KdV) equation is an integrable nonlinear partial differential equation： where is an arbitrary (nonzero) constant. See also Korteweg–de Vries equation. This
Estevez–Mansfield–Clarkson equation
The Estevez–Mansfield–Clarkson equation is a nonlinear partial differential equation introduced by Pilar Estevez, Elizabeth Mansfield, and Peter Clarkson. If U is a function of some other variables x,