Search results

Page title matches

• Hartree equation
  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 kerne
  3 KB (469 words) - 17:30, 9 July 2007
• NLS equation
  #REDIRECT [[Semilinear Schrodinger equation]]
  45 bytes (4 words) - 03:05, 29 July 2006
• Zakharov equation
  29 bytes (3 words) - 06:34, 27 July 2006
• Einstein equation
  32 bytes (3 words) - 00:45, 10 August 2006
• Maxwell equation
  31 bytes (3 words) - 07:09, 31 July 2006
• Airy equation
  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
• Schrodinger equation with potential
  The theory of the '''Schrodinger equation with potential'''
  285 bytes (43 words) - 04:51, 4 August 2006
• Kadomtsev-Petviashvili equation
  ...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 ferro
  3 KB (527 words) - 19:46, 3 February 2011
• Wave maps equation
  23 bytes (3 words) - 06:38, 29 July 2006
• Yang-Mills equation
  34 bytes (3 words) - 15:45, 5 May 2007
• Free Schrodinger equation
  The '''free Schrodinger equation''' ...dimensions. One can also consider the inhomogeneous (forced) Schrodinger equation
  2 KB (307 words) - 07:45, 15 June 2009
• Magnetic Zakharov equation
  38 bytes (4 words) - 17:01, 30 July 2006
• Free wave equation
  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
• Klein-Gordon equation
  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 normalize
  1 KB (169 words) - 20:56, 10 June 2007
• Maxwell-Dirac equation
  29 bytes (3 words) - 22:12, 3 September 2007
• Nonlinear Dirac equation
  29 bytes (3 words) - 22:12, 3 September 2007
• Minimal surface equation
  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
• Euler-Lagrange equation
  ...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 b
  657 bytes (95 words) - 20:14, 11 June 2007
• Sine-Gordon equation
  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
• Vlasov-Maxwell equation
  ...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

• Fully nonlinear
  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
• Other equations
  * The [[Ginsberg-Landau-Schrodinger equation]] * The [[Benjamin-Ono equation]]
  832 bytes (85 words) - 14:27, 9 August 2006
• Vanishing mass limit
  ...e vanishing mass limit of the [[Klein-Gordon equation]] is the [[free wave equation]].
  261 bytes (40 words) - 04:52, 4 August 2006
• Sch1998
  ...proximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation
  262 bytes (28 words) - 20:59, 17 June 2009
• ZkTkh1979
  ...valence of a nonlinear Schrödinger equation and a Heisenberg ferromagnetic equation
  267 bytes (32 words) - 00:13, 11 July 2009
• HaNm2002
  ...dified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation
  297 bytes (36 words) - 00:10, 24 May 2009
• NaTkTs2001
  ...near estimates related with the KdV equation and the nonlinear Schrödinger equation
  317 bytes (37 words) - 18:01, 10 June 2009
• Klein-Gordon equation
  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 normalize
  1 KB (169 words) - 20:56, 10 June 2007
• Large period limit
  ...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 limit
  430 bytes (70 words) - 04:56, 4 August 2006
• Completely integrable
  ...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 posed
  1 KB (166 words) - 08:40, 4 February 2011
• Sine-Gordon equation
  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
• Wed2000
  ...equation on the line and inverse scattering for the nonlinear Schrodinger equation with a potential
  319 bytes (42 words) - 20:26, 6 July 2009
• Transform
  ...operation which converts solutions of one equation to solutions of another equation. Usually one only works with transforms which are given explicitly by an a
  302 bytes (43 words) - 00:13, 15 August 2006
• Euler-Lagrange equation
  ...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 b
  657 bytes (95 words) - 20:14, 11 June 2007
• Variational method
  ...the presence of non-compact symmetries (or approximate symmetries) in the equation and in the functional, however this can sometimes be counteracted using [[c
  899 bytes (129 words) - 01:41, 15 August 2006
• Minimal surface equation
  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
• High-frequency limit
  ...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 usually
  867 bytes (126 words) - 20:02, 5 August 2006
• Dissipation
  ...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-H
  869 bytes (123 words) - 01:19, 15 August 2006
• Airy equation
  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
• Scattering
  ...asymptotically as <math>t \to \pm \infty</math> to solutions of the linear equation. Scattering can be formalized by rigorous results establishing the existen
  394 bytes (54 words) - 21:11, 9 August 2006