An auxiliary ordinary differential equation and the exp-function method

AbstractIn this paper, the new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary ordinary differential equation are derived by using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with aid of the auxiliary ordinary differential equation. As examples, the classical KdV equation, Boussinesq equation, (3+1)-dimensional Jimbo–Miwa equation and Benjamin–Bona–Mahony equation are discussed and the exact solutions are derived

Quantized Feedback Control of Network Empowerment Ammunition with Data-Rate Limitations

This paper investigates quantized feedback control problems for network empowerment ammunition, where the sensors and the controller are connected by a digital communication network with data-rate limitations. Different from the existing ones, a new bit-allocation algorithm on the basis of the singular values of the plant matrix is proposed to encode the plant states. A lower bound on the data rate is presented to ensure stabilization of the unstable plant. It is shown in our results that, the algorithm can be employed for the more general case. An illustrative example is given to demonstrate the effectiveness of the proposed algorithm