摘要
为了得到修正的VN方程组的精确解,利用改进的CK直接方法研究该方程组,建立了该方程组新、旧解之间的关系,基于此关系推广了方程组的解;同时,得到了该方程组的对称,通过求解约化方程,得到修正的VN方程组的许多新的精确解,包括幂级数解、艾米尔函数解、雅克比椭圆函数解等。结果表明,改进的CK直接方法对于求解此类非线性发展方程的精确解是有效的。
To get new exact solutions of the mVN system,a relationship was constructed between the new solutions and the old ones of the mVN system,by using an improved direct CK method.Based on the relationship,new solutions were obtained by using agiven solution of the equation.At the same time,the symmetry of the mVN system was also obtained.By solving the reduction equation,some kinds of explicit solutions of the mVN system were obtained,including the power series solution,the Airy function solution and Jacobi elliptic function solution.The results show that the improved direct CK method is effective to solve nonlinear evolution equations.
出处
《中国科技论文》
CAS
北大核心
2016年第5期538-544,共7页
China Sciencepaper
基金
国家自然科学基金资助项目(11471152)