Primitive potentials and bounded solutions of the KdV equation

S. Dyachenko, D. Zakharov, V. Zakharov

Результат исследований: Вклад в журналСтатьярецензирование

17 Цитирования (Scopus)

Аннотация

We construct a broad class of bounded potentials of the one-dimensional Schrödinger 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 Hölder 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.

Язык оригиналаАнглийский
Страницы (с-по)148-156
Число страниц9
ЖурналPhysica D: Nonlinear Phenomena
Том333
DOI
СостояниеОпубликовано - 15 окт. 2016
Опубликовано для внешнего пользованияДа

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