Preface
Chapter1SomePhysicalModelsWhichYieldTwoClassesofSingularTravellingWaveSystems
1.1Nonlinearwaveequationshavingthefirstclassofsingularnonlineartravellingwavesystems
1.2Nonlinearwaveequationshavingthesecondclassofsingularnonlineartravellingwaveequations
Chapter2DynamicsofSolutionsofSingularTravellingSystems
2.1Somepreliminaryknowledgeofdynamicalsystems
2.2Phaseportraitsoftravellingwavesystemshavingsingularstraightlines
2.3Dynamicalbehavioroforbitsinneighborhoodsofthesingular
straightline:thecaseof$1,2aresaddlepoints
2.4Dynamicalbehavioroforbitsinneighborhoodsofthesingularstraightline:thecaseof$1,2arenodepoints
2.5Dynamicalbehavioroforbitsdividedbythesingularcurves:
singulartravellingwavesystemsofthesecondclass
Chapter3ExactTravellingWaveSolutionsandTheirBifurcationsfortheKudryashov-SinelshchikovEquation
3.1Bifurcationsofphaseportraitsofsystem(3.0.4)
3.2Exacttravellingwavesolutionsfor/---3,-4
3.3Exacttravellingwavesolutionsfor/---1,2
Chapter4BifurcationsofTravellingWaveSolutionsofGeneralizedCamassa-HolmEquation(I)
4.1Bifurcationsofphaseportraitsof(4.0.2)
4.2Theexactparametricrepresentationsoftravellingwavesolutionsof(4.0.1)
4.3Theexistenceofsmoothsolitarywavesolutionsandperiodicwavesolutions
Chapter5BifurcationsofTravellingWaveSolutionsofHigherOrderKorteweg-DeVriesEquations
5.1TravellingwavesolutionsofthesecondorderKorteweg-DeVriesequationintheparameterconditiongroup(I)
5.2TravellingwavesolutionsofthesecondorderKorteweg-DeVries
equationintheparameterconditiongroup(II)
5.3TravellingwavesolutionsforthegeneralizationformofmodifiedKorteweg-DeVriesequation
Chapter6TheBifurcationsoftheTravellingWaveSolutionsofK(m,n)Equation
6.1Bifurcationsofphaseportraitsofsystem(6.0.2)
6.2Someexactexplicitparametricrepresentationsoftravellingwavesolutions
6.3Existenceofsmoothandnon-smoothsolitarywaveandperiodicwavesolutions
6.4Theexistenceofuncountablyinfinitemanybreakingwave
solutionsandconvergenceofsmoothandnon-smoothtravelling
wavesolutionsasparametersarevaried
Chapter7KinkWaveSolutionsDeterminedbyaParabolaSolutionofPlanarDynamicalSystems
7.1Sixclassesofnonlinearwaveequations
7.2Existenceofparabolasolutionsof(7.1.2)andtheirparametricrepresentations
7.3Kinkwavesolutionsfor6classesofnonlinearwaveequations
Chapter8ExactDarkSoliton,PeriodicSolutionsandChaoticDynamics
inaPerturbedGeneralizedNonlinearSchrhdingerEquation
8.1Theexactsolutionsof(8.0.2)forthecubicNLSequationwithf(q)=aq
8.2Theexactsolutionsof(8.0.2)forthecubic-quinticNLSequationwithf(q)=cqq2
8.3Thepersistenceofdarksolitionfortheperturbedcubic-quinticNLSequation(8.0.12)withoutthetermV(x)u
8.4Chaoticbehaviorofthetravellingwavesolutionsfortheperturbedcubic-quinticNLSequation(8.0.12)
Chapter9BifurcationsandSomeExactTravellingWaveSolutionsofaGeneralizedCamassa-HolmEquation(II)
9.1Bifurcationsofphaseportraitsof(9.0.5)
9.2Someexacttravellingwavesolutionof(9.0.2)inthesymmetrycases.
9.3Theexacttravellingwavesolutionsofequation(9.0.2)inanon-symmetriccase
Chapter10BifurcationsofBreatherSolutionsofSomeNonlinearWaveEquations
10.1Introduction
10.2Bifurcationsoftravellingwavesolutionsofsystem(10.1.7)whenVRp(0,r)givenby(10.1.2)
10.3Travellingwavesolutionsofsystem(10.1.1)withVap(0,r)givenby(10.1.2)
10.4Bifurcationsofsolutionsof(10.1.7)withVRp(0,r)givenby(10.1.3).
10.5Travellingwavesolutionsof(10.1.1)withVRP(O,r)givenby(10.1.3)
10.6Bifurcationsofbreathersolutionsof(10.1.4)
Chapter11BoundedSolutionsof(n+1)-dimensionalSine-andSinh-GordonEquations
11.1(n+1)-dimensionalSine-andSinh-Gordonequations
11.2Theboundedsolutionsofthesystems(11.1.4)and(11.1.5)
11.3Theboundedtravellingwavesolutionsoftheform(ll.l.2a)of(ll.l.la)
Chapter12ExactLoopSolutionsandTheirDynamicsofSomeNonlinearWaveEquations
12.1Theelasticbeamequation
12.2ThereducedOstrovskyequation
12.3Theshortpulseequation
12.4Morenonlinearwaveequationswhichhavebreakingloop-solutions-.
Chapter13ExactSolitaryWave,PeriodicandQuasi-periodicWaveSolutionsfortheKdV6Equations
13.1Theequilibriumpointsandlinearizedsystemsof(13.0.6)
13.2Exactsolitarywaveandquasi-periodicwavesolutionsoftheCDGequation(13.0.12)
13.3ExactsolutionsoftheKaup-Kupershmidtequation(13.0.10)
13.4ExactsolutionsoftheKdV6equation(13.0.2)
13.5ExactsolutionsoftheKdV6equation(13.0.3)
Chapter14ExactTravellingWaveSolutionsandTheirDynamicsforaClassCoupledNonlinearWaveEquations
14.1Exactexplicitsolutionsy=xl()of(14.0.4a)whenP(t)hasthefactorization(14.1.1)
14.2Somepropertiesofsolutionsv()ofequation(14.0.45)
Chapter15OntheTravellingWaveSolutionsforaNonlinearDiffusion-convectionEquation
15.1Thedynamicsofthetravellingwavesolutionsandtheexistenceofglobalmonotonicwavefrontsolutionsof(15.0.1)
15.2Dynamicalbehaviorofsystem(15.0.3)
15.3Exacttravellingwavesolutionsof(15.0.3)
References