The existence of solutions for the problem in the optical lattice with nonlocal nonlinearity

DOI10.1007/S10255-012-0182-2zbMath1255.35062OpenAlexW1988025106MaRDI QIDQ692712

Rui-feng Zhang, Ren-tao Liu

Publication date: 6 December 2012

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-012-0182-2

zbMATH Keywords

contraction mapping principleGalerkin methodCauchy problemglobal solutionone space dimensionPDE-ODE systemKerr-type nonlinear mediauniform priori estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• The global attractors for the dissipative generalized Hasegawa-Mima equation
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Steady state solutions for nonlinear Schrödinger equation arising in optics
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