Some results on standing wave solutions for a class of quasilinear Schrödinger equations

2019 ◽  
Vol 60 (9) ◽  
pp. 091506 ◽  
Author(s):  
Jianhua Chen ◽  
Xianjiu Huang ◽  
Bitao Cheng ◽  
Chuanxi Zhu
Keyword(s):  
Standing Wave ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wave Solutions

scholarly journals Parametrizations of the Poisson–Schrödinger equations in spherical symmetry

2021 ◽  
pp. 1-12
Author(s):  
Alan R. Parry
Keyword(s):  
Standing Wave ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Continuous Variables ◽  
Discrete Variable ◽  
Asymptotically Flat ◽  
Discrete Parameter ◽  
Minimum Value ◽  
Wave Solutions ◽  
Klein Gordon

We consider the asymptotically flat standing wave solutions to the Poisson–Schrödinger system of equations. These equations are also known as the Schrödinger–Newton equations and are the Newtonian limit of the Einstein–Klein–Gordon equations. The asymptotically flat standing wave solutions to the Poisson–Schrödinger equations are known as static states. These solutions can be parametrized using a variety of choices of two continuous parameters and one discrete parameter, each having a useful physical-geometrical interpretation. The values of the discrete variable determines the number of nodes (zeros) in the solution. We use numerical inversion techniques to analyze transformations between various informative choices of parametrization by relating each of them to a standard set of three parameters. Based on our computations, we propose explicit formulas for these relationships. Our computations also show that for the standard choice of continuous variables, the zero-node ground state yields a minimum value of a geometrically natural discrete variable. We give an explicit formula for this minimum value. We use these results to confirm two related observations from previous work by the author and others, and suggest additional applications and approaches to understand these phenomena analytically.

Solutions of perturbed Schrödinger equations with electromagnetic fields and critical nonlinearity

2010 ◽  
Vol 54 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Sihua Liang ◽  
Jihui Zhang
Keyword(s):  
Standing Wave ◽  
Electromagnetic Fields ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Critical Nonlinearity ◽  
Existence And Multiplicity ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Image Position

AbstractWe consider the existence and multiplicity of standing-wave solutionsof nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearityUnder suitable assumptions, we prove that it has at least one solution and that, for any m ∈ ℕ, it has at least m pairs of solutions.

Sign in / Sign up

Export Citation Format

Share Document