In this paper, we will construct the solution of Landau-Ginzburg equation by Adomian decomposition method. This method avoids linearization space and discretization time, it often gives a good approximation exact solution.

Attractivity of the Ginz-burg-Landau mode distribution for a pattern forming system with marginally stable long modes. Justification of the 2D NLS equation – Quadratic resonances do not matter in case of analytic initial conditions. Justification of the Nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. approximation of time osc...

In conventional micromagnetism magnetic domain configurations are calculated based on a continuum theory for the magnetization. This theory assumes that the absolute magnetization value is constant in space and time. Dynamics is usually described with the Landau-Lifshitz-Gilbert LLG equation, the stochastic variant of which includes finite temperatures. Using simulation techniques with atomisti...

In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method for the non cut-off Boltzmann equation in the spirit of [21, 23]. We show that the kernel modes that define the spectral method have the correct grazing collis...

In this paper, we study the solution of the fractional nonlinear Ginzburg-Landau(FNGL) equation with weak initial data in the weighted Lebesgue spaces. The existence of a solution to this equation is proved by the contraction-mapping principle.

From a variational perspective, we derive a series of magnetization and quantum spin current systems coupled via an “s-d” potential term, including Schrödinger-Landau-LifshitzMaxwell system, Pauli-Landau-Lifshitz system, and Schrödinger-Landau-Lifshitz system with successive simplifications. For the latter two systems, we propose to use the time splitting spectral method for the quantum spin cu...