【摘要】：b族方程概括了一大類淺水波動(dòng)力學(xué)問(wèn)題,研究發(fā)現(xiàn)其中的Camassa-Holm方程(b=2)和Degasperis-Procesi方程(b=3)均存在穩(wěn)定傳播的尖波解。在已有b族方程統(tǒng)一對(duì)稱形式的基礎(chǔ)上,針對(duì)b=0這一特殊情形,構(gòu)造了一種等價(jià)于多辛Box格式的新隱式多辛格式,用于探索這一特殊情形下b族方程是否存在穩(wěn)定傳播的尖波解。通過(guò)數(shù)值模擬,一方面,驗(yàn)證了構(gòu)造的隱式多辛格式具有很好的保結(jié)構(gòu)性能和良好的長(zhǎng)時(shí)間數(shù)值穩(wěn)定性;另一方面,從數(shù)值模擬結(jié)果中發(fā)現(xiàn)在b=0這一特殊情形下,b族方程不存在穩(wěn)定傳播的尖波解。
[Abstract]:A large class of wave mechanics problems in shallow water are generalized by B-family equations. It is found that both the Camassa-Holm equation (bn _ 2) and the Degasperis-Procesi equation (n _ 3) have sharp wave solutions for stable propagation. On the basis of the unified symmetric form of the B-family equation, a new implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed for the special case of BX _ 0. It is used to explore whether there is a sharp wave solution for the stable propagation of the b family equation in this special case. Through numerical simulation, on the one hand, it is verified that the implicit multi-symplectic scheme has good guaranteed structure performance and good numerical stability for a long time. On the other hand, from the numerical simulation results, it is found that there is no sharp wave solution for the stable propagation of the b family equation under the special case of BX 0.
【作者單位】： 西北工業(yè)大學(xué)理學(xué)院;西北工業(yè)大學(xué)力學(xué)與土木建筑學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(11672233、11302169、11372253) 陜西省自然科學(xué)基金(2015JM1026) 航天支撐技術(shù)基金(2015-HT-XGD)資助
【分類號(hào)】：O175
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本文編號(hào)：2364212