The b-family equation, which contains a general family of shallow water wave equations with the different values of b, has shown the so-called peaked wave solutions with the cases when b=2 (Camassa-Holm equation) and b=3 (Degasperis-Procesi equation).To explore whether a special case when b=0 exists the stable peaked solution, based on the multi-symplectic form, the multi-symplectic Box scheme to construct a new implicit scheme is applied focusing on this case.The numerical experiments show that the constructed scheme has well structure-preserving property and good long time numerical stability.Furthermore, we can also find that there do not exist the stable propagation of peaked solution from the numerical results in the special case when b=0.%b族方程概括了一大类浅水波动力学问题,研究发现其中的Camassa-Holm方程(b=2)和Degasperis-Procesi方程(b=3)均存在稳定传播的尖波解.在已有b族方程统一对称形式的基础上,针对b=0这一特殊情形,构造了一种等价于多辛Box格式的新隐式多辛格式,用于探索这一特殊情形下b族方程是否存在稳定传播的尖波解.通过数值模拟,一方面,验证了构造的隐式多辛格式具有很好的保结构性能和良好的长时间数值稳定性;另一方面,从数值模拟结果中发现在b=0这一特殊情形下,b族方程不存在稳定传播的尖波解.
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