摘要
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。
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 so- lution, 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-pre- serving 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.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2017年第2期321-325,共5页
Journal of Northwestern Polytechnical University
基金
国家自然科学基金(11672233
11302169
11372253)
陕西省自然科学基金(2015JM1026)
航天支撑技术基金(2015-HT-XGD)资助
关键词
b族方程
多辛方法
尖波解
守恒律
b-family equation
multi-symplectic method
peaked solution
conservation law
