scholarly journals Asymptotic stability of small gap solitons in nonlinear Dirac equations

2012 ◽  
Vol 53 (7) ◽  
pp. 073705 ◽  
Author(s):  
Dmitry E. Pelinovsky ◽  
Atanas Stefanov
Keyword(s):  
Asymptotic Stability ◽  
Dirac Equations ◽  
Nonlinear Dirac Equations ◽  
Gap Solitons

scholarly journals Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Initial Value Problem ◽  
Strong Solutions ◽  
Representation Formula ◽  
Critical Space ◽  
Lebesgue Spaces ◽  
Initial Value ◽  
Dirac Equations ◽  
Nonlinear Dirac Equations ◽  
Global Strong Solutions ◽  
Solution Representation

We study the initial value problem of some nonlinear Dirac equations which areLmℝcritical. Corresponding to the structure of nonlinear terms, global strong solutions can be obtained in different Lebesgue spaces by using solution representation formula. The uniqueness of weak solutions is proved for the solutionU∈L∞0,T; Ym+2ℝ.

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