【摘要】 利用微分形式的吴方法计算了Benney方程的势对称及其不变解.由于Benney方程中包含不稳定项和耗散项,使得直接求其不变解较为困难,利用吴-微分特征列算法可大大降低其中确定方程组的计算难度.本文全面讨论了Benney方程不同系数情况下的对称,并且得到了新的势对称,同时利用这些对称求得了相应的不变解,这些解对进一步研究Benney方程所描述的物理现象具有广泛的应用价值.文章表明,对于守恒形式的偏微分方程,可通过其辅助系统求得的势对称来构造其不变解.更多还原

【Abstract】 The potential symmetries and invariant solutions of Benney equation were calculated by differential form Wu’s method.It was difficult to obtain the invariant solutions of Benney equation directly due to the unstable term and dissipative term involved in Benney equation.The calculating difficulty of determining equations can be greatly decreased by using Wuwen-tsun-Differential Characteristic Algorithm.In this paper,the symmetries of Benney equation with different coefficients were fully discussed,and new potential symmetries were obtained.Furthermore,the corresponding invariant solutions can be obtained by using the above symmetries.The solutions had extensive application value for further researching the physical phenomena described by Benney equation.The research indicates that the invariant solutions of conserved partial differential equations can be constructed by using the potential symmetries,which are derived from their auxiliary system.更多还原