The Travelling Wave Solutions Of A Class Nonlinear Schrodlinger Equation And The Hidden Attractor Of A Class Chua’s System Study

Nonlinear science is a subject which established during the study of nonlinear phenomenon. We know many practical phenomena and problems can be described by nonlinear equation. Nonlinear wave equation as a very important branch of nonlinear science fields, there are a lot of wave process in nature and technology can be described by nonlinear wave equation. Thus this is still a challenging and important task to research the exact traveling wave solutions of nonlinear wave equations. As we all know the vibration phenomenon can cause unnecessary loss in our life and productive activity. Recently, some researchers find that there are not only self-excited vibration in dynamical systems, but also hidden attractors as well, which is difficult to find. Therefore, study the hidden attractor about nonlinear dynamical system not only has very important academic significance but also has very important realistic meanings to the life.This paper is divided into two parts:The major work of the first part considers the generalized nonlinear Schrodinger equation with physical background and introduce the "three-step" method for solving the nonlinear equation ,which proposed by professor Li Jibin . The exact travelling wave solutions for the Schrodinger equation by using dynamical system method. The exact parametric representations of bright and dark solitary wave solutions, kink and anti kink wave solution, as well as periodic wave solutions are obtained under different parameter conditions.The second part mainly introduces the hidden attractor. We all know the classical attractors of the Chua’s are those excited from unstable equilibria. However, there is another form of attractor-hidden attractors, its domain of attraction does not contain neighborhoods of equilibria. This paper considers the Chua’s system which the nonlinear is continuously, and the system has one stable zero equilibrium FO and two saddle equilibria S1 and S2.Then applied the new analytical numerical method, introduced the describing function.Therefore, we can find the hidden attractor of this kind of Chua’s system.