Aunifiedperturbationtheoryisdevelopedhereforcalculatingsolitarywavesofallheightsbyseriesexpansionofbaseflowvariablesinpowersofasmallbaseparametertoeighteenthorderfortheone-parameterfamilyofsolutionsinexactform,withallthecoefficientsdeterminedinrationalnumbers.Comparativestudiesarepursuedtoinvestigatetheeffectsduetochangesofbaseparameterson(i)theaccuracyofthetheoreticallypredictedwavepropertiesand(ii)therateofconvergenceofperturbationexpansion.Twoimportantresultsarefoundbycomparisonsbetweenthetheoreticalpredictionsbasedonasetofparametersseparatelyadoptedforexpansioninturn.First,theaccuracyandtheconvergenceoftheperturbationexpansions,appraisedversustheexactsolutionprovidedbyanearlierpaper[1]asthestandardreference,arefoundtodepend,quitesensitively,onchangesinbaseparameter.Theresultingvariationsinthesolutionarephysicallydisplayedinvariouswavepropertieswithdifferencesfounddependentonwhichproperty(e.g.thewaveamplitude,speed,itsprofile,excessmass,momentum,andenergy),onwhatrangeinvalueofthebase,andontherankoftheordernintheexpansionbeingaddressed.Secondly,regardingconvergence,thepresentperturbationseriesisfounddefinitelyasymptoticinnature,withtherelativeerrorδ(n)(therelativemean-squaredifferencebetweensuccessiveordersnofwaveelevations)reachingaminimum,δm,ataspecificorder,n=nm,bothdependingonthebaseadopted,e.g.n=11-12basedonparameterα(waveamplitude),nm,β=15onβ(amplitude-speedsquareratio),andnm.∈=17on∈(wavenumbersquared).Theasymptoticrangeisbroughttocompletionbythehighestorderofn=18reachedinthiswork.
