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On the N-waves hierarchy with constant boundary conditions. Spectral properties
International Journal of Geometric Methods in Modern Physics ( IF 2.1 ) Pub Date : 2024-04-13 , DOI: 10.1142/s0219887824400152
Vladimir S. Gerdjikov 1, 2 , Georgi G. Grahovski 3
Affiliation  

This paper is devoted to N-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators L, whose potentials Q(x,t) tend to constants Q± for x±. For special choices of Q±, we outline the spectral properties of L, the direct scattering transform and construct its fundamental analytic solutions. We generalize Wronskian relations for the case of CBC — this allows us to analyze the mapping between the scattering data and the x-derivative of the potential Qx. Next, using the Wronskian relations, we derive the dispersion laws for the N-wave hierarchy and describe the NLEE related to the given Lax operator.



中文翻译:

具有恒定边界条件的 N 波层次。光谱特性

本文致力于-与辛李代数相关的具有恒定边界条件的波动方程。我们研究一类 Lax 算子的谱特性L,其潜力X,t趋向于常数±为了X±无穷大。对于特殊选择±,我们概述了光谱特性L,直接散射变换并构造其基本解析解。我们将 Wronskian 关系推广到 CBC 的情况——这使我们能够分析散射数据和X-势能的导数X。接下来,使用朗斯基关系,我们推导出色散定律-wave 层次结构并描述与给定 Lax 算子相关的 NLEE。

更新日期:2024-04-15
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