孤立子、非线性发展方程和逆散射（英文版）

AnexcitingandextremelyactiveareaofresearchinvestigationduringthepasttwentyyearshasbeenthestudyofSolitonsandtherelatedissueoftheconstructionofsolutionstoawideclassofnonlinearequations.Indeedtherehavebeenafewbookswrittenwhichservetoreviewaspectofthisburgeoningfield.Abookcoauthoredbyoneofus(MJA)exactlytenyearsago,discussedmanyoftherelevantviewpointsaswellasavarietyofapplications.CertainimportantandnovelsubareasofresearchsuchasthetheapplicationoftheInverseScatteringTransform(I.S.T.)tosolvenonlinearwaveequationsontheinfiniteinterval,inonespatialandonetemporaldimension(1+1),weredescribedindetail.Atthattimethecompleteinversescatteringmethodologyhadbeencarriedoutprimarilyforthosenonlinearequationsrelatedtosecondorderscatteringproblems.Althoughitwasknownthatcertainnonlinearevolutionequationsinoneandtwospatialdimensionswererelatedtosuitable(higherorderandtwodimensional)linearscatteringproblems,andspecialtechniqueswereavailable,neverthelessitwasnotyetclearthataunifiedandeffectiveprocedurecouldbeappliedtoallofthesenonlinearequations.ThemainpurposeofthisbookisthedescriptionofhowtheI.S.T.techniquecanbeappliedtothesesituations.