正则长波方程的对称约化、精确解和守恒律

Symmetry Reductions,Exact Solutions and the Conservation Laws of The Regularized Long Wave Equation

利用直接对称的方法研究了正则长波方程,首先求出方程的李点对称及最优系统,其次将正则长波方程约化成常微分方程,进一步结合齐次平衡原理、Riccati方程展开法和幂级数展开法对约化方程求精确解,进而得到该方程的精确解.最后给出正则长波方程的伴随方程和守恒律.

In this paper,we studied the regularized long wave （RLW） equation by using the direct sym metry method. First,we derived the point symmetry and the optimal system of the equation, then we reduced the regularized long wave equation to ordinary differential equations （ODEs）. Furthermore,we pro- vided the exact solutions of the reduced ordinary differential equations by the homogeneous balance principle （HBP）,Riccati equation expansion method and power series expansion method,thus,the exact solutions of original equation were obtained. Finally, we presented the adjoint equation and the conservation laws of the regularized long wave equation.