systems, the three-wave equations, sometimes called the three-wave resonant interaction equations or triad resonances, describe small-amplitude waves in a variety...

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e...

physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium...

a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric...

The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system.: 1–2  Its...

one-way wave equation is a first-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity...

In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg–de Vries equation. These solutions are in terms of the...

of three or more waves, which includes the "three-wave equation" Quantum mechanics Wave equation Quantum state Matter wave Flint H.T., (1929) Wave Mechanics...

the wave equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for...

they provide a pair of invariants or conserved quantities for the three-wave equation. For example, in a resonant interaction in non-linear optics, the...

Rogue wave Scattering Shallow water equations Shive wave machine Sound Standing wave Transmission medium Velocity factor Wave equation Wave power Wave turbulence...

non-linear optics, and described by a class of solutions to the three-wave equation. Sometimes, the scattering is more or less isotropic, i.e. the incoming...

the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces....

Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on...

The Benjamin–Bona–Mahony equation (BBM equation, also regularized long-wave equation; RLWE) is the partial differential equation u t + u x + u u x − u x...

equation Nonlinear sigma models Sine–Gordon equation Thirring model Three-wave equation Integrable PDEs in 2 + 1 dimensions Davey–Stewartson equation...

of substantial contemporary interest. The model hyperbolic equation is the wave equation. In one spatial dimension, this is ∂ 2 u ∂ t 2 = c 2 ∂ 2 u ∂...

field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were...

guiding waves in terms of a relativistic wave equation were unsuccessful until in 1926 Schrödinger developed his non-relativistic wave equation. He further...

differential equation on the space of three-dimensional spatial metrics. The Wheeler–DeWitt equation has the form of an operator acting on a wave functional;...

element analysis. Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of...

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...

component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant...

phenomenon in a wave tank and named it the "Wave of Translation". The Korteweg–de Vries equation was later formulated to model such waves, and the term...

solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as...

three-dimensional space. While periodic travelling waves have been known as solutions of the wave equation since the 18th century, their study in nonlinear...

rogue waves. Among other causes, studies of nonlinear waves such as the Peregrine soliton, and waves modeled by the nonlinear Schrödinger equation (NLS)...

one-dimensional wave equation, and within ten years Euler discovered the three-dimensional wave equation. The Euler–Lagrange equation was developed in...

waves, they should satisfy some sort of wave equation. Inspired by Debye's remark, Erwin Schrödinger decided to find a proper three-dimensional wave equation...

spacetime. The corresponding equation is a relativistic wave equation called the Proca equation. The Proca action and equation are named after Romanian physicist...