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Initial Value Problems for Integrable Systems on a Semi-Strip
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Initial Value Problems for Integrable Systems on a Semi-Strip
Інший ID:
2010 Mathematics Subject Classification: 35Q55; 35Q60; 34B20; 35A02
DOI:10.3842/SIGMA.2016.001
DOI:10.3842/SIGMA.2016.001
Посилання:
Initial Value Problems for Integrable Systems on a Semi-Strip / A.L. Sakhnovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 60 назв. — англ.
Підтримка:
This research was supported by the Austrian Science Fund (FWF) under Grant No. P24301.
The author is grateful to A. Rainer for a helpful discussion on quasi-analytic functions.
Дата:
2016
Переглядів:
578
Завантажень:
265
Анотація:
Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonlinear Schrödinger equation.) Next, a special case of the nonlinear optics (N-wave) equation is considered.
