Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations
Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations
复制标题
高维混合色散非线性薛定谔方程：理论分析和数值计算
DOI：
10.1088/1751-8121/ac7019
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kevrekidis, Panayotis G
中科院分区：
文献类型：
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作者：
Stefanov, Atanas;Tsolias, Georgios A;Cuevas-Maraver, Jesús;Kevrekidis, Panayotis G
在目前的工作中，我们提供了一个高维非线性Schrödinger类的二次四次模型的基态表征，该模型结合了聚焦双调和算子与各向同性或各向异性离焦拉普拉斯算子（在线性水平上）和幂律非线性。主要考察了维数d= 2的典型例子，我们发现在三次和五次情况之间的拉普拉斯函数超过一定的阈值系数时，不稳定性产生，而对于三次以下的幂，所有解都是稳定的。在五次以上，直到临界非线性指数p，稳定频率的范围逐渐缩小。最后，在临界p以上，所有解都是不稳定的。在各向异性的情况下，情况非常相似，不同之处在于，即使在三次情况之前，数值计算表明了一个不稳定频率的间隔。我们的分析推广了拉普拉斯前因子b和非线性幂p任意组合的相关观察结果。
In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schrödinger class with a combination of a focusing biharmonic operator with either an isotropic or an anisotropic defocusing Laplacian operator (at the linear level) and power-law nonlinearity. Examining principally the prototypical example of dimension d= 2, we find that instability arises beyond a certain threshold coefficient of the Laplacian between the cubic and quintic cases, while all solutions are stable for powers below the cubic. Above the quintic, and up to a critical nonlinearity exponent p, there exists a progressively narrowing range of stable frequencies. Finally, above the critical p all solutions are unstable. The picture is rather similar in the anisotropic case, with the difference that even before the cubic case, the numerical computations suggest an interval of unstable frequencies. Our analysis generalizes the relevant observations for arbitrary combinations of Laplacian prefactor b and nonlinearity power p.