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bokomslag Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability
Vetenskap & teknik

Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability

Guoping Zhang Alexander Pankov

Inbunden

2649:-

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  • 400 sidor
  • 2025
The book is devoted to rigorous mathematical results on discrete nonlinear Schrdinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations emerge as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there is necessary material from the spectral theory of discrete Schrdinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.
  • Författare: Guoping Zhang, Alexander Pankov
  • Format: Inbunden
  • ISBN: 9789811290275
  • Språk: Engelska
  • Antal sidor: 400
  • Utgivningsdatum: 2025-06-30
  • Förlag: World Scientific Publishing Co Pte Ltd