摘要利用Galerkin方法证明了一类半线性耦合Schro¨dinger方程组解的存在唯一性.In this paper, we prove the existence and uniqueness of solution of a class of coupled Semilinear cquations by using the Galerkin Method.
1Infed E, Rowlands G. Nonlinear Waves, Solitons and Chaos[M]. Cambridge : Cambridge Univ Press, 1990 : 298 - 328.
2Glassey R T. On the blowing up of solution to the Cauchy problem for nonlinear Schrodinger equations[J] .J Math Phys, 1977,18(9) :1794- 1797.
3Tsutsumi M. Nonexistence of global solutions to the Cauchy problem for nonlinear Schrodinger equations[J]. Comm Math Phys, 1999.81:467 - 476.
4Ginibre J,Velo G. On a class of nonlinear Schrodinger equations theory,general case[J] .J Funct Anal, 1979,32:33- 71.
5Weinstein M I. Nonlinear Schrodinger equations and sharp interpolations estimates[J]. Comm Math Phys , 1983,87:567 - 567.
6Shatah J,Strauss W. Instability of nonlinear bound states[J]. Comm Math Phys, 1985,100:173 - 190.
7Otis C, Wright M, Gregory Forest. On the Backlund - gage transformation and homoclinic orbits of a coupled nonlinear Schrodinger system[J]. Physica, 2000 :104 - 106.
2uoBoling. The global exeistence and unqueness of SchrOdingger-KDV equations[J]. ActMath Sinica .1998.
3GuoBoling The global exeistence and unoueness of Maxwell-SchrOdinggererequations[J]. Act Math Sinica. 1998.
4Otis C,Wright.M ,Gregory Forest On the Backlund-gage transformation and homoclinic orbits of a coupled nonlinear SchrOdingger system Physica[J]. D[4](2000) 104- 116.
5P.J.Olver,Application of Lic Group to Differential Equations[J]. Berlin,Springer 1986.
6D. David , M. v. Tratanik. Physica[J]. D61 (1991)308.