Remarks on the orbital stability of ground state solutions of fKdV and related equations

分数阶KdV和NLS方程周期波形的稳定性

Stability of periodic waves for the fractional KdV and NLS equations

本文针对分数阶KdV和NLS方程，构造了哈密顿量约束极小化的钟形周期波，并严格证明了其非退化性、谱稳定性和轨道稳定性。

Remarks on solitary waves and Cauchy problem for a Half-wave-Schrödinger equations

In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schrödinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist and converge to zero as the velocity tends to $1$. Finally, we solve the Cauchy problem for initial data in $L^{2}_{x}H^{s}_{y}(\mathbb{R}^{2})$, with $s>\frac{1}{2}$.

A New Method to prove the Existence, Non-existence, Multiplicity, Uniqueness, and Orbital Stability/Instability of standing waves for NLS with partial confinement

We give a new method to prove the existence, non-existence, multiplicity, orbital stability/instability of standing waves for NLS with partial confinement without the subcritical hypothesis, even in the reduction equation. Using this method, we give an affirmative answer for an open problem proposed by [7, Remark 1.10] where the authors conjectured the existence of more than a normalized solution. We also establish uniqueness results of the ground state solutions depending on the bifurcation parameters. We explain that when the effect of partial confinement is strong, a dimension reduction app…