scholarly journals Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions

2007 ◽  
Vol 326 (2) ◽  
pp. 1001-1006 ◽  
Author(s):  
Ji Shu ◽  
Jian Zhang
Keyword(s):  
Global Existence ◽  
Second Order ◽  
Nonlinear Schrödinger Equations ◽  
Order Derivative ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Sharp Condition ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Two Space Dimensions

scholarly journals Strong Instability of Solitary Waves for Inhomogeneous Nonlinear Schrödinger Equations

2021 ◽  
Author(s):  
chenglin Wang ◽  
Jian Zhang
Keyword(s):  
Global Existence ◽  
Solitary Waves ◽  
Nonlinear Schrödinger Equations ◽  
Laser Beams ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Sharp Condition ◽  
Nonlinear Schrödinger ◽  
Strong Instability ◽  
Nonlinear Schrodinger Equations

This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross-constrained variational method, a sharp condition for global existence is derived. Then, by solving a variational problem, the strong instability of solitary waves of this equation is proved.

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