耦合 Burgers 方程的 CTE 可积性及精确解

摘要

借助符号计算软件 Maple，利用 CTE 方法验证了耦合 Burgers 方程的 CTE 可积性，得到了耦合 Burgers 方程的孤子和其他波的相互作用解，包括孤子和椭圆余弦波作用解、共振多孤子解、孤子和误差函数波作用解、孤子和有理波作用解、孤子和周期波作用解。最后给出了孤子和椭圆余弦波作用解及共振多孤子解所对应的图形。%With the help of symbolic computation software Maple,by using the CTE method,a coupled Burgers equation was proved to be CTE solvable.Many interaction solutions among solitons and other types of nonlinear excitations of the coupled Burgers equation were obtained,which include soliton-cnoidal waves,multiple resonant solutions,soliton-error function waves,soliton-rational waves,and soliton-periodic waves.The corresponding graphs of the soliton-cnoidal waves and multiple resonant solutions were presented.