Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability
Series: Series On Analysis, Applications And Computation; 13;
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56 437 Ft
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Product details:
- Publisher World Scientific
- Date of Publication 31 January 2027
- ISBN 9789811290275
- Binding Hardback
- No. of pages400 pp pages
- Language English 0
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Long description:
The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger 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 Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.
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