Application of quasi-continuum models for perturbation analysis of discrete kinks

作者：Andrianov Igor V^*; Kholod Elena G; Weichert Dieter

来源：Nonlinear Dynamics, 2012, 68(1-2): 1-5.

DOI：10.1007/s11071-011-0198-9

• Kink
• Improved continuum model
• Sine-Gordon equation
• Phi(4) model
• Pade approximants

Here, we study a relation between discrete and continuum models on an example of the sine-Gordon and Phi(4) equations. The analysis of various receptions of continualization in a linear case is carried out. The best approach allowing describing all spectrum of the discrete one-dimensional medium is chosen. Also, the nonlinear discrete sine-Gordon and Phi(4) models are analyzed. The possibility of improvement of the known continuum approximations of these equations is shown.