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The dynamic behavior of phase synchronization in coupled oscillators is investigated using Lyapunov exponents and correlation function. A strongest chaotic phase synchronization——complete synchronization was observed, in which the first two transverse Lyapunov exponents are made equal and the projective structures of oscillators become exactly the same.

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In this paper, a non-linear (3+1)-dimensional Zakharov-Kuznetsov equation is investigated by employing the subsidiary equation method, which arises in quantum magneto plasma. The periodic solutions, rational wave solutions, soliton solutions for the quantum Zakharov-Kuznetsov equation which play an important role in mathematical physics are obtained with the help of the Riccati equation expan?sion method. Meanwhile, the electrostatic potential can be accordingly obtained. Compared to the other methods, the exact solutions obtained will extend on earlier reports by using the Riccati equation.

Constructing infinite sequence exact solutions of nonlinear evolution equations *Taogetusang( ) a)b) † and Narenmandula( ) c)