کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1895926 1044401 2012 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs
چکیده انگلیسی

We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve 3×3 matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse Scattering Transform (IST), the presence of a boundary presents new challenges. Over the last fifteen years, an extension of the IST formalism developed by Fokas and his collaborators has been successful in analyzing boundary value problems for several of the most important integrable equations with 2×2 Lax pairs, such as the Korteweg–de Vries, the nonlinear Schrödinger, and the sine-Gordon equations. In this paper, we extend these ideas to the case of equations with Lax pairs involving 3×3 matrices.


► We present a method for analyzing initial-boundary value problems for integrable equations.
► The equations have Lax pairs involving 3×3 matrices.
► The solution is given in terms of the solution of a Riemann–Hilbert problem.
► We show how to characterize the unknown boundary values.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 241, Issue 8, 15 April 2012, Pages 857–875
نویسندگان
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