A note on the two-dimensional Ginzburg-Landau equation for directional, nearly monochromatic waves

作者：Nohara BT^*

来源：Nonlinear Dynamics, 2003, 33(4): 431-442.

DOI：10.1023/B:NODY.0000009938.47271.6e

• amplitude modulation
• directional
• nearly monochromatic waves
• Ginzburg-Landau equation
• Schrodinger equation
• Schrodinger-Nohara equation

In this paper we deal with the two-dimensional Ginzburg - Landau equation. First we simply expand the one-dimensional Ginzburg - Landau equation to the two-dimensional one. Then the concept of the directionality is imported into the two-dimensional Ginzburg - Landau equation. Directional, nearly monochromatic waves have a fixed wavenumber but spread over some propagation area in propagating directions. Moreover, most of the energy of waves is concentrated in a single propagating direction. In slightly unstable, directional, nearly monochromatic waves, the fact that the envelope surface created by the amplitude modulation is presented by the product of the solution of the Schrodinger - Nohara equation and the time function is shown. In the nonlinear case, the time function depends on space.

• 出版日期2003-9