New Weierstrass Semi-rational Expansion Method to Doubly Periodic Solutions of Soliton Equations

Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.

标量波量子技术在环境、能源、生物医学等领域的应用与实践

物理学家们已经注意到经典物理中的麦克斯韦方程组及薛定谔方程式中所没有解释的能量场的存在,但这种新型能量场还未被广泛关注及应用。本文主要介绍了标量波量子技术目前在环境水处理等领域的应用,标量波发生装置的试验,以及将来在能源工业以及医疗行业的潜在应用和问题做了详细的讨论。