We extend Lou's direct perturbation
method for solving the nonlinear Schrödinger equation to the case of
the derivative nonlinear Schrödinger equation (DNLSE). By applying
this method, different types of perturbation solutions are obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of
perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method. 相似文献
Immiscible polymer blends are an important family of polymer materials. The interfacial thickness between different phases is a very important parameter that dictates, to a great extent, the morphology and properties of such a blend. This work explores and optimizes an up-to-date atomic force microscopy (AFM) of type NanoIR2? system in order to quantitatively measure the interfacial thickness of immiscible polymer blends. This system is equipped with two nano-probes capable of detecting the response of a material to an infrared pulse called AFM-infrared spectroscopy mode (AFM-IR) or conducting resonance called AFM-Lorentz Contact Resonance mode (AFM-LCR), respectively. Its potential for quantitatively measuring the interfacial thickness of immiscible polymer blends is evaluated using blends composed of polyamide 6 (PA6) and polyolefin elastomer (POE) in the presence or absence of a POE containing maleic anhydride (POE-g-MAH) as a compatibilizer. Surface roughness affects adversely the signal intensity and consequently an accurate measurement of the interfacial thickness. Optimum sample surface preparation procedures are proposed.
Hermitian and skew-Hermitian splitting (HSS) method converges unconditionally, which is efficient and robust for solving non-Hermitian positive-definite systems of linear equations. For solving systems of nonlinear equations with non-Hermitian positive-definite Jacobian matrices, Bai and Guo proposed the Newton-HSS method and gave numerical comparisons to show that the Newton-HSS method is superior to the Newton-USOR, the Newton-GMRES and the Newton-GCG methods. Recently, Wu and Chen proposed the modified Newton-HSS (MN-HSS) method which outperformed the Newton-HSS method. In this paper, we will establish a new accelerated modified Newton-HSS (AMN-HSS) method and give the local convergence theorem. Moreover, numerical results show that the AMN-HSS method outperforms the MN-HSS method. 相似文献