A CROSS-CONSTRAINED VARIATIONAL PROBLEM FOR THE GENERALIZED DAVEY STEWARTSON SYSTEM

作者：Gan Zaihui^*; Zhang Jian

来源：Proceedings of the Edinburgh Mathematical Society, 2009, 52(01): 67-77.

DOI：10.1017/S0013091506000794

• generalized Davey Stewartson system
• cross-constrained variational problem
• sharp threshold
• global existence
• blow-up
• instability

We study the sharp threshold for blow-up and global existence and the instability of standing wave e(iwt)u(omega)(x) for the Davey Stewartson system
i phi(t) Delta phi a vertical bar phi vertical bar(2)phi E(1)(vertical bar phi vertical bar(2))phi - 0 (DS)
in R(3), where u(omega) is a ground state. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we derive a sharp criterion for global existence and blow-up of the solutions to (DS), which can be used to show that there exist blow-up solutions of (DS) arbitrarily close to the standing waves.

• 出版日期2009-2
• 单位四川师范大学