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- The '''Hartree equation''' is of the form ...c Schrodinger equation; the [[cubic NLS]] is in some sense a limit of this equation as <math>n \rightarrow d,</math> (after suitable normalization of the kerne3 KB (469 words) - 17:30, 9 July 2007
- #REDIRECT [[Semilinear Schrodinger equation]]45 bytes (4 words) - 03:05, 29 July 2006
- 29 bytes (3 words) - 06:34, 27 July 2006
- 32 bytes (3 words) - 00:45, 10 August 2006
- 31 bytes (3 words) - 07:09, 31 July 2006
- The (homogeneous) '''Airy equation''' is given by ...tions. One such problem is the reduced (or linearized) [[Korteweg-de Vries equation]]1 KB (214 words) - 22:11, 19 January 2018
- The theory of the '''Schrodinger equation with potential'''285 bytes (43 words) - 04:51, 4 August 2006
- ...equation]], and when <math>\lambda > 0</math> the equation is the [[KP-II equation]]. These equations are a model for shallow long waves in the x direction, ...varying amplitude, weak non-linearity) one can obtain the Davey-Stewatson equation (formally, at least). KP-I also arises as a model for sound waves in ferro3 KB (527 words) - 19:46, 3 February 2011
- 23 bytes (3 words) - 06:38, 29 July 2006
- 34 bytes (3 words) - 15:45, 5 May 2007
- The '''free Schrodinger equation''' ...dimensions. One can also consider the inhomogeneous (forced) Schrodinger equation2 KB (307 words) - 07:45, 15 June 2009
- 38 bytes (4 words) - 17:01, 30 July 2006
- The '''free wave equation''' on <math>{\mathbb R}^{1+d}</math> is given by One can add a mass term to create the [[Klein-Gordon equation]].2 KB (358 words) - 16:00, 1 July 2018
- The '''Klein-Gordon equation''' is given by [[Minkowski space]]. When the mass is zero this is just the [[free wave equation]]. When the mass is positive, one usually rescales spacetime to normalize1 KB (169 words) - 20:56, 10 June 2007
- 29 bytes (3 words) - 22:12, 3 September 2007
- 29 bytes (3 words) - 22:12, 3 September 2007
- The (hyperbolic) '''minimal surface equation''' takes the form ...n \times R</math> ). This is the Minkowski analogue of the minimal surface equation in Euclidean space, see [[Hp1994]].809 bytes (125 words) - 22:10, 10 April 2007
- ...ints of that functional. It can be computed formally by starting with the equation ...iltonian]] can (in principle, at least) be expressed as the Euler-Lagrange equation of a functional, and conversely Euler-Lagrange equations can in principle b657 bytes (95 words) - 20:14, 11 June 2007
- The '''sine-Gordon equation''' ...ontinuum of pendula hanging from a wire. It is a [[completely integrable]] equation, and has many interesting solutions, including "breather" solutions.705 bytes (103 words) - 23:39, 22 January 2009
- ...nt the electromagnetic field. x and v live in R^3 and t lives in R. This equation is a coupled wave and conservation law system, and models collision-less pl ...\rho</math>. Considerably more is known for the existence theory of this equation.2 KB (297 words) - 13:33, 11 July 2007
Page text matches
- A '''fully nonlinear''' equation takes the form for some nonlinear function ''F''. By differentiating this equation once and working with the system <math>v := (u, Du)</math>386 bytes (62 words) - 00:46, 8 August 2006
- * The [[Ginsberg-Landau-Schrodinger equation]] * The [[Benjamin-Ono equation]]832 bytes (85 words) - 14:27, 9 August 2006
- ...e vanishing mass limit of the [[Klein-Gordon equation]] is the [[free wave equation]].261 bytes (40 words) - 04:52, 4 August 2006
- ...proximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation262 bytes (28 words) - 20:59, 17 June 2009
- ...valence of a nonlinear Schrödinger equation and a Heisenberg ferromagnetic equation267 bytes (32 words) - 00:13, 11 July 2009
- ...dified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation297 bytes (36 words) - 00:10, 24 May 2009
- ...near estimates related with the KdV equation and the nonlinear Schrödinger equation317 bytes (37 words) - 18:01, 10 June 2009
- The '''Klein-Gordon equation''' is given by [[Minkowski space]]. When the mass is zero this is just the [[free wave equation]]. When the mass is positive, one usually rescales spacetime to normalize1 KB (169 words) - 20:56, 10 June 2007
- ...tion on the non-periodic domain <math>\mathbf{R}^d</math>, though when the equation has [[infinite speed of propagation]] then the justification of this limit430 bytes (70 words) - 04:56, 4 August 2006
- ...ely integrable in the sense that there exist a Lax pair formulation of the equation. a completely integrable equation. Some nonlinear PDE's as the KdV posed1 KB (166 words) - 08:40, 4 February 2011
- The '''sine-Gordon equation''' ...ontinuum of pendula hanging from a wire. It is a [[completely integrable]] equation, and has many interesting solutions, including "breather" solutions.705 bytes (103 words) - 23:39, 22 January 2009
- ...equation on the line and inverse scattering for the nonlinear Schrodinger equation with a potential319 bytes (42 words) - 20:26, 6 July 2009
- ...operation which converts solutions of one equation to solutions of another equation. Usually one only works with transforms which are given explicitly by an a302 bytes (43 words) - 00:13, 15 August 2006
- ...ints of that functional. It can be computed formally by starting with the equation ...iltonian]] can (in principle, at least) be expressed as the Euler-Lagrange equation of a functional, and conversely Euler-Lagrange equations can in principle b657 bytes (95 words) - 20:14, 11 June 2007
- ...the presence of non-compact symmetries (or approximate symmetries) in the equation and in the functional, however this can sometimes be counteracted using [[c899 bytes (129 words) - 01:41, 15 August 2006
- The (hyperbolic) '''minimal surface equation''' takes the form ...n \times R</math> ). This is the Minkowski analogue of the minimal surface equation in Euclidean space, see [[Hp1994]].809 bytes (125 words) - 22:10, 10 April 2007
- ...lize the solutions to have frequency comparable to one. In that case, the equation acquires a rescaling parameter <math>\hbar</math>, and the limit is usually867 bytes (126 words) - 20:02, 5 August 2006
- ...forward in time. The model instance of a dissipative equation is the heat equation ...ispersive equations are often [[Hamiltonian]] and are the [[Euler-Lagrange equation]] for some [[variational problem]], dissipative equations are usually non-H869 bytes (123 words) - 01:19, 15 August 2006
- The (homogeneous) '''Airy equation''' is given by ...tions. One such problem is the reduced (or linearized) [[Korteweg-de Vries equation]]1 KB (214 words) - 22:11, 19 January 2018
- ...asymptotically as <math>t \to \pm \infty</math> to solutions of the linear equation. Scattering can be formalized by rigorous results establishing the existen394 bytes (54 words) - 21:11, 9 August 2006