On the study of properties of solutions to partial differential equations

1.我们引入了一个新的相函数，并证明了具有亚临界非线性项的非局部非线性薛定谔方程的解的时间渐近性。这些结果发表在《美国数学》杂志上，1998年发表在《数学》杂志上。在Hokkaido Math.J.1998和Dis.Conti.dya.Sys.1999中，我们利用一些解析函数空间将这些结果推广到具有亚临界功率非线性项的局部非线性薛定谔方程。2.通过研究Ary函数的性质，我们研究了J.Funct.Anal.1998中广义Korteweg-de Vries方程的解的时间渐近性。我们还在1999年的《国际数学研究通告》中证明了修正的Kortweg-de Vries方程的修正散射态的存在性。修正的Bejinamin-Ono方程是著名的非线性色散方程之一。在Trans.A.M.S.1999中，我们通过引入一个新的相函数证明了修正散射态的存在

1.We introduced a new phase function and showed asymptotic behavior in time of solutions to nonlocal nonlinear Schrodinger equations with sub-critical nonlinearities. These results have been published in Amer.J.Math.1998, SUT J.Math.1998. In Hokkaido Math .J.1998 and Dis.Conti.Dyna.Sys.1999 we extended these results to local nonlinear Schrodinger equations with sub-critical power nonlinearities by making use of some analytic function spaces.2.We studied asymptotic behavior in time of solutions to generalized Korteweg-de Vries equations in J.Funct.Anal.1998 by investigating the property of Airy function. We also proved the existence of the modified scattering states of modified Kortweg-de Vries equation in International Mathematics Research Notices, 1999.3.Modified Beinjamin-Ono is known as one of the well known nonlinear dispersive equations. In Trans.A.M.S.1999 we showed the existence of modified scattering states by introducing a new phase function