Domain Structure Formation in Designing of the Opened Informative Measuring Systems

Abstract

The opened systems possess an increasing significance and possibilities of applying in designing of measuring devices. Now an essentially nonlinear models are used for such systems. The perturbation approach is not enough for these purposes. Models of new types have solutions in a form of soliton or kink and similar objects. The equation of Fisher–Kolmogorov–Petrovskii–Piskunov is one of such equations. This equation is used for description of convection-reaction-diffusion processes. Such processes are used for studying of a self-organisation and formation of a structure in non-equilibrium opened systems. The aim of this work was to construct of a new solution for the modified equation of Fisher–Kolmogorov– Petrovskii–Piskunov in which a space inhomogeneity is accounted.To solve this problem the direct Hirota method for nonlinear partial differential equation is applied.Some modifications into this method were introduced.The new topologically non-trivial solution of the modified Fisher–Kolmogorov–Petrovskii–Piskunov equation is constructed explicitly. This solution has a kink-like form. Some arguments on the stability of such solution are considered.A possibility of domain structure formation in the systems which describe by the Fisher–Kolmogorov– Petrovskii–Piskunov equation is demonstrated.

Keywords

• fisher–kolmogorov–petrovskii–piskunov equation
• hirota method
• kink