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Long time dynamics and coherent states in nonlinear wave equations. (English) Zbl 1397.35160

Melnik, Roderick (ed.) et al., Recent progress and modern challenges in applied mathematics, modeling and computational science. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-6968-5/hbk; 978-1-4939-6969-2/ebook). Fields Institute Communications 79, 59-88 (2017).
The author discuss some recent new progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.
For the entire collection see [Zbl 1381.00028].

MSC:

35L90 Abstract hyperbolic equations
35L05 Wave equation
35Q55 NLS equations (nonlinear Schrödinger equations)
35L72 Second-order quasilinear hyperbolic equations
35P25 Scattering theory for PDEs
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
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References:

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