Nonstandard bilinearization and interaction phenomenon for PT-symmetric coupled nonlocal nonlinear Schrödinger equations

2020 ◽  
Vol 103 ◽  
pp. 106209 ◽  
Author(s):  
Fajun Yu ◽  
Rui Fan
Keyword(s):  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Nonlocal Nonlinear ◽  
Interaction Phenomenon

Collapse for the Generalized Three-Dimensional Nonlocal Nonlinear Schrödinger Equations

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Xin Jiang ◽  
Zaihui Gan
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Three Dimensional ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Nonlocal Terms ◽  
Nonlocal Nonlinear

AbstractFinite time collapse of solutions to the generalized three-dimensional nonlocal nonlinear Schrödinger equations is studied. This result is achieved through establishing some a priori estimates for the nonlocal terms and by introducing a type of virial identities.

scholarly journals On a class of nonlocal nonlinear Schrödinger equations with potential well

2019 ◽  
Vol 9 (1) ◽  
pp. 665-689 ◽  
Author(s):  
Tsung-fang Wu
Keyword(s):  
Eigenvalue Problems ◽  
Nehari Manifold ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Asymptotic Results ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Nehari Manifold ◽  
Nonlocal Nonlinear

Abstract In this paper we investigate the existence, multiplicity and asymptotic behavior of positive solution for the nonlocal nonlinear Schrödinger equations. We exploiting the relationship between the Nehari manifold and eigenvalue problems to discuss how the Nehari manifold changes as parameters μ, λ changes and show how existence, multiplicity and asymptotic results for positive solutions of the equation are linked to properties of the manifold.

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