Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation
Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation
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DOI：
10.1088/1751-8113/48/38/385202
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
B. Feng;Junchao Chen;Yong Chen;K. Maruno;Y. Ohta
中科院分区：
文献类型：
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作者：
B. Feng;Junchao Chen;Yong Chen;K. Maruno;Y. Ohta
本文构造了耦合短脉冲（CSP）方程的可积半离散和全离散模拟。构造的关键是CSP方程解的双线性形式和行列式结构。我们还构造了N-孤子解的半离散和完全离散的类似物的CSP方程的Casorati行列式的形式。在连续极限下，证明了全离散CSP方程收敛于半离散CSP方程，进而收敛于连续CSP方程。此外，CSP方程的可积半离散化被用作数值模拟的自适应移动网格方法。数值结果与解析结果吻合得很好。
In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.