Affiliations: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560‐0043, Japan E‐mail: nhayashi@math.wani.osaka‐u.ac.jp | Departamento de Ciencias Básicas, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México E‐mail: kaikina@ifm1.ifm.umich.mx | Instituto de Física y Matemáticas, Universidad Michoacana, AP 2‐82, CP 58040, Morelia, Michoacán, México E‐mail: pavelni@zeus.ccu.umich.mx
Abstract: We obtain the large time asymptotic expansion of small solutions to the Landau–Ginzburg type equations \[\cases{u_{t}-\alpha u_{xx}+\beta |u|^{2}u=0,\quad x\in {\mathbf{R}},\ t>0,\cr \noalign{\vskip3pt}u(0,x)=\phi (x),\quad x\in {\mathbf{R}},\cr}\] where α,β∈C,Rα>0, R(β/$\sqrt{2|\alpha |^{2}+\alpha ^{2}}$)≥0, under the condition that the initial data ϕ are sufficiently small in a suitable weighted norm and the mean value ∫ϕ(x) dx≠0.
