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We study the orbitally stability of standing waves for the L2$$ {L}^2 $$‐critical inhomogeneous combined source term fractional nonlinear Schrödinger equation: i∂tu−(−Δ)su+a|x|−b|u|pu+|u|4sNu=0,(t,x)∈ℝ×ℝN$$ i{\partial}_tu-{\left(-\Delta \right)}^su+a{\left|x\right|}^{-b}{\left|u\right|}^pu+{\left|u\right|}^{\frac{4s}{N}}u=0,\left(t,x\right)\in \mathrm{\mathbb{R}}\times {\mathrm{\mathbb{R}}}^N $$where N2N−1

This article studies the Schrödinger equation with an inhomogeneous combined term i ∂ t u − (− Δ) s u + λ 1 | x | − b | u | p u + λ 2 | u | q u = 0 , where s ∈ (1 2 , 1) , λ 1 , λ 2 = ± 1 , 0 < b < { 2 s , N } and p , q > 0 . We study the limit behaviour of the infinite blow-up solution at the blow-up time. When the parameters p , q , λ 1 and λ 2 have different values, we obtain the nonexistence of a strong limit for the non-radial solution and the L 2 concentration for the radial solution. Interestingly, we find that the mass of the finite time blow-up solutions are concentrated in different ways for different parameters. [ABSTRACT FROM AUTHOR]

For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for constructing a dynamic S-Box based on the new model is proposed. Through aperiodic evaluation and statistical complexity measurement, it is shown that the compound chaotic system has features such as complex structure and stronger randomness than classical chaotic systems. Based on the chaotic sequence generated by the composite system, we design a dynamic S-Box generation mechanism. The mechanism can quickly generate high-security S-Boxes. Then, an example of randomly generating S-Boxes is given alongside an analytical evaluation of S-Box standard performance criteria such as bijection, boomerang uniformity, bit independence, nonlinearity, linear approximate probability, strict avalanche effect, differential uniformity, the and generalized majority logic criterion. The evaluation results confirm that the performance of the S-Box is excellent. Thus, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the blow‐up dynamics of L2−critical focusing inhomogeneous fractional nonlinear Schrödinger equation: i∂tu−(−Δ)su+|x|−b|u|2σu=0,(t,x)∈R×RN,with 0

This paper deals with the local existence and uniqueness of strong solutions for the generalized Boussinesq equations with fractional dissipation. As a corollary, we establish some regularity criteria to guarantee smoothness of solutions. [ABSTRACT FROM AUTHOR]