【摘要】 对高阶非线性方程的可积性研究仍是一大难点。通过贝尔多项式方法对6阶Kd V方程进行可积性研究和求解。首先通过构造贝尔多项式的几种组合,推导出带有辅助自变量的双线性形式,进而求得该方程的N孤子解。基于贝尔多项式形式的双线性形式,通过符号计算,得到方程的Bcklund变换,Lax对和无穷守恒律。更多还原

【Abstract】 The integrability and solution of sixth-order Korteweg-de Vries( Kd V) equation is studied by Bell-polynomial method. By constructing several combinations of Bell polynomials, the bilinear form with an auxiliary argument is deduced,and the N-soliton solution of this equation is obtained. Based on the bilinear form of the Bell-polynomial form,Bcklund transformation,Lax pair and infinite numbers of conservation laws of the equation are derived by symbolic computation.更多还原