科研之友
微信
新浪微博
Facebook
分享链接
摘要
We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iq(t)(x,t)= -q(xx)(x,t)+(rq(2))(x) on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter This problem has explicit (x, t) dependence, and it has jumps across {xi is an element of C vertical bar Im xi(4) = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a(xi), b(xi)}, {A(xi), B (xi)}, and {A(xi), B(xi)}, which in turn are defined in terms of the initial data q(0)(x) = q(x, 0), the boundary data g(0)(t) = q(0, t), g(1)(t) = q(x)(0, t), and another boundary values f(0)(t) = q(L, t), f(1)(t) = q(x) (L, t). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
- 出版日期2014-7
- 单位复旦大学
