充分非線性發(fā)展方程的Compacton解及其穩(wěn)定性.pdf

1、江蘇大學碩士學位論文充分非線性發(fā)展方程的Compacton解及其穩(wěn)定性姓名：于水猛申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：田立新20050301江蘇大學碩士學位論文AbstractInthispapertntrodueingtheconceptofnonlinearintensity，westudyexactsolutions(Cempactonsolutions，Peakansolutions，Kinksolutions，bell—

2、shapedsolitarysolutions)ofsornefullynonlinearevolutionaryequationsThenconsidertheirHamiltonstructuremadsomeconservationlawsAtlastWeprovethatlinearstabilityofallCompaetonsolutionsInthethirdchapter，westudygeneralizedfullyn

3、onlinearfifth—orderKdVequationWeobtainPeakonsolutionsbydirectmethodandCompactunsolutionsbyansatzsmethodFmthermorewestudyitin(21)，(31)andhigherdimensionsGivingasimilarfifthorderequationwhichderivedfromLagrangian，obtainHam

4、iltonSgP2cturoandsomeconservmionLawsAtlastWeprovethestabilityofCompactonsolutionbylinearstabilitytheoryInthefonhchapterweintroducethenonlinearintensityKlein—GordontypeequationandbyusingimprovedgeneralizedprojectiveRiccat

5、iequationmethod，weobtainabundantexactsolutions(kinksolutions，singularkinksolutionsandperiodicsolutions)ofthenonlinearintensityKlein—Gordon—typeequationWeusetheansatzsmethodandobtainthemulti—compactonsolutionsThen，wediscu

6、ssthechangesofCompaetonsohthonswithvariousnonlinearintensityparametersandconsidertheCompactorsolutionsofhigherdimensionsnonlinearintensityKleinGordontypeequationInthefifthchapter，weresearchgeneralizednonlinearZakharovKuz

7、netsovequationandobtainmultieompactonsolutionsbyansatzsmethodParticularlyweobtainnewcompactonsolutionsofthegeneralizednonlinearZakharov—KuznetsovequationbylinearmethodInthesixthchapter，westudygeneralizedBBMequationFirst，

8、wegivethreeconservationlawsofBBMequationThenweobtainexactsolutionsbyvariable—coefficientbalancingactmethod，andfurtherstudythemulticompactunsolutionsandsolitarywavesolutionsofthegeneralizedBBMequationKeywords：fullynonline