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Riemannθ函数得到了Fokas-Lenells方程的代数几何解的表示.
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 Riemannθfunction.
出处
《数学年刊（A辑）》
CSCD
北大核心
2012年第2期135-148,共14页
Chinese Annals of Mathematics
基金
国家自然科学基金(N0.51109031
No.11026165
No.50909017
No.50921001)
教育部博士点基金(No.20100041120037)资助的项目
