Primitive potentials and bounded solutions of the KdV equation
Primitive potentials and bounded solutions of the KdV equation
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DOI：
10.1016/j.physd.2016.04.002
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发表时间：
2016-10-15
影响因子：
4
通讯作者：
Zakharov, V.
中科院分区：
文献类型：
--
作者：
Dyachenko, S.;Zakharov, D.;Zakharov, V.
我们构造了一维薛定谔算子的一类有界势，它们具有。与周期性有限间隙势相同的谱结构，但既不是周期性的也不是准周期性的。这种势，我们称之为原语，是由在允许带上定义的一对正 Holder 连续函数非唯一参数化的。原势被构造为奇异积分方程组的解，可以有效地进行数值求解。模拟表明这些势可能具有无序结构。原势生成 KdV 层次结构的一大类有界非零解，我们将它们解释为 KdV 方程框架中可积湍流的示例。 (C) 2016 Elsevier B.V. 保留所有权利。
We construct a broad class of bounded potentials of the one-dimensional Schrodinger operator that have the. same spectral structure as periodic finite-gap potentials, but that are neither periodic nor quasi-periodic. Such potentials, which we call primitive, are non-uniquely parametrized by a pair of positive Holder continuous functions defined on the allowed bands. Primitive potentials are constructed as solutions of a system of singular integral equations, which can be efficiently solved numerically. Simulations show that these potentials can have a disordered structure. Primitive potentials generate a broad class of bounded non-vanishing solutions of the KdV hierarchy, and we interpret them as an example of integrable turbulence in the framework of the KdV equation. (C) 2016 Elsevier B.V. All rights reserved.