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Ginzburg-Landau equation

Ginzburg-Landau equation
Order	2nd
Solvable	Partially solvable
First derived by	Ginzburg and Landau (1950)

Contents 1 Ginzburg-Landau equation 1.1 Definition 1.2 History 1.3 Solutions 1.3.1 Type of a solution 1.4 Integrals of motion 1.5 Lax pairs 1.6 Lagrangian 1.7 Hamiltonian 1.8 Applications and connections 1.9 The Cauchy problem 1.10 Variations 1.11 See also 1.12 References 1.13 External links

Definition

$$A_t=\left(1+ib\right)\Delta A+\epsilon A-\left(1-ic\right){\left|A\right|}^{2}A$$

History

Solutions

Type of a solution

Integrals of motion

Lax pairs

Lagrangian

Hamiltonian

Applications and connections

The Cauchy problem

Variations

See also

References

1. Kudryashov N.A. Analytical theory of nonlinear differential equations (in Russian) // 2^nd ed., Institute of Computer Investigation, Moscow-Izhevsk, 2004. — 360 p.
2. Kudryashov N.A. Methods of nonlinear mathematical physics (in Russian) // Moscow Engineering Physics Institute, Moscow, 2008. — 352 p.

External links

1. Ginzburg–Landau theory in Wikipedia, the free encyclopedia
2. Ginzburg-Landau equation in Wolfram MathWorld