论文标题
小型解决方案的全球动力学对修改的分数Korteweg-de Vries和非线性Schrödinger方程
Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schrödinger equations
论文作者
论文摘要
本文涉及经过修改的分数Korteweg-de Vries（修饰的FKDV）和非线性Schrödinger（修改的FNLS）方程，分别分别| d |^α\ partial_x和| d | d |^{α+1}。我们证明了针对修饰的FKDV和FNLS方程的库奇问题的全球溶液存在，并具有具有对数相校正的修改散射。我们的结果涵盖了修改后的FKDV和FNLS方程的全范围-1 <α<1，α\ neq 0。
This paper concerns the modified fractional Korteweg-de Vries (modified fKdV) and nonlinear Schrödinger (modified fNLS) equations, with the dispersions |D|^α\partial_x and |D|^{α+1}, respectively. We prove the global existence of small solutions for both the Cauchy problems to the modified fKdV and fNLS equations, with a modified scattering which has a logarithmic phase correction. Our results cover the full range -1<α<1, α\neq 0 for both the modified fKdV and fNLS equations.
