Jiuli Yin

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We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ∼ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we(More)
We present a KdV-like 2-parameter equation u t + (3(1 − δ)u + (δ + 1) uxx ux)u x = ϵu xxx. By using the dynamical system method, existence of different traveling wave solutions are discussed, including smooth solitary wave solution of with bell type, solitary wave solutions of valley type and peakon wave solution of valley type. Numerical integration are(More)
Lattice models are associated with rather important problems in physics. Solution of these models gives insights into the nature of phase transitions, magnetization and scaling behavior, as well as insights into the nature of quantum field theory. An expanded G'/G-expansion method is presented to seek explicit solutions of nonlinear lattice equations. The(More)
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