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008 201021s2020 si ob 001 0 eng
040 _a WSPC
_b eng
_c WSPC
010 _z 2020043383
020 _a9789811227912
_q(ebook)
020 _z9789811227905
_q(hbk.)
050 0 4 _aQC174.26.W28
_b.C36 2020
072 7 _aMAT
_x007020
_2bisacsh
072 7 _aSCI
_x040000
_2bisacsh
072 7 _aMAT
_x007000
_2bisacsh
082 0 4 _a530.124
_223
100 1 _aCarles, Rémi.
_921182
245 1 0 _aSemi-classical analysis for nonlinear Schrödinger equations
_h[electronic resource] :
_bWKB analysis, focal points, coherent states /
_cby Rémi Carles.
250 _a2nd edition.
260 _aSingapore :
_bWorld Scientific,
_c2020.
300 _a1 online resource (xiv, 352 p.)
520 _a"The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent. Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrödinger equations in negative order Sobolev spaces. The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform"--Publisher's website.
505 0 _aWKB analysis. Preliminary analysis. Weakly nonlinear geometric optics. Convergence of quadratic observables via modulated energy functionals. Pointwise description of the wave function. Some instability phenomena -- Caustic crossing : the case of focal points. Caustic crossing : formal analysis. Focal point withtout external potential. Focal point in the presence of an external potential. Some ideas for supercritical cases -- Coherent states. The linear case. Nonlinear coherent states : main tools. Power-like nonlinearity. Hartree-type nonlinearity.
504 _aIncludes bibliographical references and index.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader.
650 0 _aSchrödinger equation.
_915839
650 0 _aNonlinear theories.
_93339
655 0 _aElectronic books.
_93294
856 4 0 _uhttps://www.worldscientific.com/worldscibooks/10.1142/12030#t=toc
_zAccess to full text is restricted to subscribers.
942 _cEBK
999 _c72762
_d72762