Instituto de Física, Departamento de Física Química, Universidad Nacional Autónoma de México, México.
Chaos. 2011 Sep;21(3):033120. doi: 10.1063/1.3629985.
We analyze the response of rational and regular (hyperbolic-secant) soliton solutions of an extended nonlinear Schrödinger equation (NLSE) which includes an additional self-defocusing quadratic term, to periodic modulations of the coefficient in front of this term. Using the variational approximation (VA) with rational and hyperbolic trial functions, we transform this NLSE into Hamiltonian dynamical systems which give rise to chaotic solutions. The presence of chaos in the variational solutions is corroborated by calculating their power spectra and the correlation dimension of the Poincaré maps. This chaotic behavior (predicted by the VA) is not observed in the direct numerical solutions of the NLSE when rational initial conditions are used. The solitary-wave solutions generated by these initial conditions gradually decay under the action of the nonlinearity management. On the contrary, the solutions of the NLSE with exponentially localized initial conditions are robust solitary-waves with oscillations consistent with a chaotic or a complex quasiperiodic behavior.
我们分析了包含额外自散焦二次项的扩展非线性薛定谔方程（NLSE）的理性和规则（双曲正割）孤子解对该项系数的周期性调制的响应。使用有理和双曲试探函数的变分近似（VA），我们将这个 NLSE 转化为哈密顿动力系统，这些系统产生混沌解。通过计算它们的功率谱和庞加莱映射的关联维数，证实了变分解中的混沌存在。当使用理性初始条件时，NLSE 的直接数值解中不会观察到这种混沌行为（VA 预测）。由这些初始条件产生的孤波解在非线性的作用下逐渐衰减。相反，具有指数局域初始条件的 NLSE 的解是具有一致的混沌或复杂拟周期行为的鲁棒孤波。
