Manakov system with parity symmetry on nonzero background and associated boundary value problems
Manakov system with parity symmetry on nonzero background and associated boundary value problems
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DOI：
10.1088/1751-8121/ac674a
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Asela Abeya;G. Biondini;B. Prinari
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文献类型：
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作者：
Asela Abeya;G. Biondini;B. Prinari
我们描述了具有非零背景和定义良好的空间宇称对称性（即，当解的每个分量是偶数或奇数时），对应于在原点处具有Dirichlet或Neumann边界条件的半直线上的边值问题。我们确定的对称性的本征函数所产生的空间奇偶性的解决方案，我们确定相应的对称性的散射数据（反射系数，离散光谱和赋范常数）。发现所有宇称诱导的对称性比标量中的更复杂（即，单组分）情况。特别是，我们表明，产生暗孤子的离散本征值出现在对称的四重态，而那些产生暗-亮孤子的对称八重态。我们还刻画了纯偶数或纯奇数的情况下（其中两个组件是偶数或奇数的x的函数）和“混合奇偶校验”的情况下（其中一个组件是偶数，而另一个是奇数）之间的差异。最后，我们将展示如何，在每种情况下，空间对称性产生的约束可能存在的自对称本征值，对应于固定孤子，我们研究的解决方案所产生的行为。
We characterize initial value problems for the defocusing Manakov system (coupled two-component nonlinear Schrödinger equation) with nonzero background and well-defined spatial parity symmetry (i.e., when each of the components of the solution is either even or odd), corresponding to boundary value problems on the half line with Dirichlet or Neumann boundary conditions at the origin. We identify the symmetries of the eigenfunctions arising from the spatial parity of the solution, and we determine the corresponding symmetries of the scattering data (reflection coefficients, discrete spectrum and norming constants). All parity induced symmetries are found to be more complicated than in the scalar (i.e., one-component) case. In particular, we show that the discrete eigenvalues giving rise to dark solitons arise in symmetric quartets, and those giving rise to dark–bright solitons in symmetric octets. We also characterize the differences between the purely even or purely odd case (in which both components are either even or odd functions of x) and the ‘mixed parity’ cases (in which one component is even while the other is odd). Finally, we show how, in each case, the spatial symmetry yields a constraint on the possible existence of self-symmetric eigenvalues, corresponding to stationary solitons, and we study the resulting behavior of solutions.