Geodesic
Global Existence for a System of Weakly Coupled Nonlinear Schr\"{o}dinger Equations
Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 686-691

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This paper discusses the weakly coupled nonlinear Schrödinger equations in the supercritical case. With the best constant of Gagliardo–Nirenberg inequality, we derive a sufficient condition for the global existence of the solutions; this condition is expressed in terms of the stationary solutions (nonlinear ground state).
Keywords: weakly coupled nonlinear Schrödinger equations, Gagliardo–Nirenberg inequality, Cauchy problem, Laplace operator, nonlinear optics.
Mots-clés : global existence 
@article{MZM_2009_86_5_a5,
     author = {Ji Shu and Jian Zhang},
     title = {Global {Existence} for a {System} of {Weakly} {Coupled} {Nonlinear} {Schr\"{o}dinger} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {686--691},
     publisher = {mathdoc},
     volume = {86},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a5/}
}
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Ji Shu; Jian Zhang. Global Existence for a System of Weakly Coupled Nonlinear Schr\"{o}dinger Equations. Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 686-691. http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a5/