论文标题
混合色散非线性schrödinger方程在更高维度：理论分析和数值计算
Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations
论文作者
论文摘要
在目前的工作中，我们提供了非线性schr {Ö} dinger类的高维二次二次 - 四分化模型的特征，并将聚焦的双旋转型操作员与各向同性或各向异性型偶极性脱离laplacian decotoction copitian clielagian Operator（在线性级别上）和PowerLaw norlaal norlaileality。在主要检查尺寸$ d = 2 $的原型示例时，我们发现不稳定性超出了立方体和Quintic案例之间的拉普拉斯元素的一定阈值系数，而所有解决方案对于立方体以下的功率均稳定。在五重奏上方，直到关键的非线性指数$ p $，存在稳定频率逐渐变窄的范围。最后，在关键的$ p $上方所有解决方案都是不稳定的。在各向异性情况下，图片相当相似，差异甚至在立方体情况之前，数值计算表明了不稳定频率的间隔。我们的分析概括了Laplacian Prefactor $ B $和非线性功率$ P $的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 Schr{ö}dinger 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 $p$.
