We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger （NLS） equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried...We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger （NLS） equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal＇s simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.展开更多
In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial con...In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial convergence conclusion of the general heterogeneous HK dynamics.That is,there must be some agents who will reach static states in finite time,while the other opinions have to evolve between them with a minimum distance if all the opinions does not reach consensus.And this result leads to the convergence of several special cases of heterogeneous HK dynamics,including when the minimum confidence bound is large enough,the initial opinion difference is small enough,and so on.展开更多
基金supported by the Kyung Hee University on sabbatical leave in 2010
文摘We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger （NLS） equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal＇s simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.
基金supported by the National Natural Science Foundation of China(Grant No.11371049)Fundamental Research Funds for the Central Universities(Grant No.2016JBM070)
文摘In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial convergence conclusion of the general heterogeneous HK dynamics.That is,there must be some agents who will reach static states in finite time,while the other opinions have to evolve between them with a minimum distance if all the opinions does not reach consensus.And this result leads to the convergence of several special cases of heterogeneous HK dynamics,including when the minimum confidence bound is large enough,the initial opinion difference is small enough,and so on.
