we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota's bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...

As with the scalar case, the equation is satisfied only at selected values of x = r = [r1, r2, · · · , rn], called the roots. The separation process model discussed in section §1.3.1 (variations 2 and 3, in particular) and the reaction sequence model of section §1.3.5 are two of the many examples in chemical engineering that give rise to such non-linear system of equations. As with the scalar c...

∗ Division of Automatic Control Department of Electrical Engineering, Linköpings universitet, SE-581 83 Linköping, Sweden ∗∗ Department of Mechanical Science and Engineering, Nagoya University, Japan Abstract: In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for...

The satisfiability of a class of random Boolean equations named massive algebraic system septated to linear and nonlinear subproblems is studied in this paper. On one hand, the correlation between the magnetization of generators and the clustering of solutions of the linear subproblem is investigated by analyzing the Gaussian elimination process. On the other hand, the characteristics of maxima...

Cube Attack is a successful case of Algebraic Attack. Cube Attack consists of two phases, linear equation extraction and solving the extracted equation system. Due to the high complexity of equation extraction phase in finding linear equations, we can extract nonlinear ones that could be approximated to linear equations with high probability. The probabilistic equations could be considered as l...