Stability of Standing Waves for the Nonlinear Schrödinger Equation with Mixed Power-Type and Hartree-Type Nonlinearities  

作　　者：Chunyang Yan Chunyang Yan(Department of Mathematics, Northwest Normal University, Lanzhou, China)

机构地区：[1]Department of Mathematics, Northwest Normal University, Lanzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第10期3439-3457,共19页应用数学与应用物理（英文）

摘　　要：This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0,   (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,x)is a complex valued function of (t,x)∈ℝ+×ℝN. The parameters N≥3, 0p4Nand 0γmin{ 4,N }. By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0,   (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,x)is a complex valued function of (t,x)∈ℝ+×ℝN. The parameters N≥3, 0p4Nand 0γmin{ 4,N }. By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.

关 键 词：Nonlinear Schrödinger Equation Concentration Compactness Principle Orbital Stability 

分 类 号：O17[理学—数学]