| 孙玉娟,王振,张鸿庆.Fokas-Lenells方程的代数几何解[J].数学年刊A辑,2012,33(2):135~148 |
| Fokas-Lenells方程的代数几何解 |
| Algebro-Geometric Solutions to Fokas-Lenells Equation |
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| DOI： |
| 中文关键词: Fokas-Lenells方程 代数几何解 Abel-Jacobi坐标 Riemann θ函数 |
| 英文关键词:Fokas-Lenells equation, Algebro-geometric solution,
Abel-Jacobi coordinates, Riemann θ function |
| 基金项目:国家自然科学基金，教育部博士点基金 |
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| 中文摘要: |
| 从一个给定的谱问题出发,利用Lenard梯度序列推导出Fokas-Lenells方程.随后,这个方程被分解为可解的常微分方程.基于Lax矩阵的有限阶展开,引入了椭圆坐标,从而,流可以在Abel-Jacobi坐标下被拉直.最后,利用Riemann θ函数得到了Fokas- Lenells方程的代数几何解的表示. |
| 英文摘要: |
| The Fokas-Lenells equation is given by the Lenard gradient sequence for a given
spectral problem. Then, this equation is decomposed into solvable ordinary differential
equations. Based on the finite-order expansion of the Lax matrix, elliptic coordinates are
introduced. So, the flow can be straighten out by the Abel-Jacobi coordinates. At the end,
algebro-geometric solutions of the Fokas-Lenells equation are presented by means of the
Riemann θ function. |
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