非線性Klein-Gordon和非線性Schrodinger方程.pdf

1、、：i耳：!0：JS0100l置繳：一蓋鹽分類號：～0—1二羔——’1；：段代碼：!Q3四川師范大學(xué)碩學(xué)位論文非線性KleinGordon和非線性SehrSdinger方程蔣毅培養(yǎng)墮，直駕刖衄塾盔堂筮生量筮往型堂堂醫(yī)指導(dǎo)教師一菠查揸一職稱—塾握一學(xué)科專業(yè)一一基型麴堂研究方向二垣邀盆一夏捏淪z完成日期一2QQ2生生且!Q目NonlinearKlein—GordonandnonlinearSchrSdingerequationsMajorB

2、asicMathematicsGraduateJiangYiSupervisorPuZhilinAbstract：Inthispaper，westudysomepropertiesofnonlinearKleinGordonandnonlinearSchrbdingerequationswhicharemajormodelsinquantummechanics‘Inchapter1，F(xiàn)ortheCauchyproblemfortheno

3、nlinearKleinGordonequationwithpotential，wedefinenewstableandunstablesetsfortheinitialdataWeprovethatifduringtheevolutionentersintotheunstablesetthesolutionblowsupinfinitetimeIfduringtheevolutionentersintothestableset，the

4、solutionisglobalByusingscalingargument，wealsoanswerthequestionofhowsmalltheinitialdataare，theglobalsolutionoftheCanchyproblemexistsInchapter2，wediscussestheCauchyproblemofnonlinearSchrfdingerequationswefirstestablishthee

5、xistenceofstandingwaveassociatedwiththegroundstatesbyvariationalcalculusThenbythepotentialwellargumentandtheconcavitymethod，wegetasharpconditionforblowupandglobalexistencetothesolutionsoftheCauchyproblemandanswersuchapro