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的非局部非线性薛定谔方程解在时间上的渐近性。这些结果发表在《Amer.J.Math》杂志上。1998，中山大学数学研究所。在北海道数学。1998年，dis . con . dyna . sys。利用解析函数空间，将这些结果推广到具有亚临界幂非线性的局部非线性薛定谔方程。研究了广义Korteweg-de Vries方程解在时间上的渐近行为。1998年通过研究Airy函数的性质。我们也在《国际数学研究通报》1999.3中证明了修正Kortweg-de Vries方程修正散射态的存在性。修正Beinjamin-Ono方程是众所周知的非线性色散方程之一。在Trans.A.M.S。1999年我们通过引入一个新的相函数证明了修正散射态的存在性

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