Nonlinear partial differential equations | Exactly solvable models

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 The original equation studied by Bretherton has quadratic nonlinearity, Nayfeh treats the case with two different methods: Whitham's averaged Lagrangian method and the method of multiple scales. The Bretherton equation is a model equation for studying weakly-nonlinear wave dispersion. It has been used to study the interaction of harmonics by nonlinear resonance. Bretherton obtained analytic solutions in terms of Jacobi elliptic functions. (Wikipedia).

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Scalar field | Lagrangian (field theory) | Conservation law | Functional derivative | Hamiltonian system | Mathematics | Integer | Quadratic function | Partial derivative | Eulerโ€“Lagrange equation | Partial differential equation | Ali H. Nayfeh