【摘 要】
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Low-amplitude two-dimensional lattice solitons near edges of Bloch bands in periodic media were determined analytically in a recent study [1].In this talk,
【机 构】
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ZhouPei-YuanCenterforAppliedMathematics,TsinghuaUniversity,Beijing,China
【出 处】
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International Conference Nonlinear Waves-Theory and Applicat
论文部分内容阅读
Low-amplitude two-dimensional lattice solitons near edges of Bloch bands in periodic media were determined analytically in a recent study [1].In this talk, linear-stability properties of such lattice solitons near band edges are analyzed by asymptotic methods.It is shown that under focusing nonlinearity, 2D lattice solitons centered at a potential minimum are unstable if the slope of the power curve at the band edge is negative.How ever, under defocusing nonlinearity, such lattice solitons are unstable if the slope of the power curve at the band edge is positive, which is the opposite of the focusing case.The asymptotic formula for the unstable eigenvalue is also derived analytically.This analytical formula is checked against numerically computed eigenvalues, and excellent agreement is obtained.
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