Ginzburg–Landau equations induced from multi-dimensional bichromatic waves Original Research Article

In this paper we consider an envelope function for the multi-dimensional bichromatic wave View the MathML sourceub(x,t) defined by a Fourier transformation and show that it satisfies a kind of Ginzburg–Landau equation under some conditions for the spectrum function View the MathML sourceS(k) and the angular function View the MathML sourceω(k). The result is an extension of Nohara’s work [B.T. Nohara, Derivation and consideration of governing equations of envelope surface created by directional, nearly monochromatic waves, International Journal of Nonlinear Dynamics and Chaos in Engineering Systems 31 (4) (2003) 375–392; B.T. Nohara, Governing equations of envelope surface created by directional, nearly monochromatic waves, Journal of Japan Society of Industrial and Applied Mathematics 13 (2) (2003) 213–224 (in Japanese)] which treated one-dimensional wave functions.