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In this paper, the Fisher equation is analysed. One of its travelling wave solution
is obtained by comparing it with KdV--Burgers (KdVB) equation. Its amplitude, width
and speed are investigated. The instability for the higher order disturbances to the
solution of the Fisher equation is also studied. 相似文献
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利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性 Schr(o)dinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组). 相似文献
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Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice 下载免费PDF全文
Hongjuan Meng 《中国物理 B》2021,30(12):126701-126701
We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice. 相似文献
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Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong. 相似文献
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We numerically investigate the nonlinear waves propagating in a one-dimensional particle chain when the damping effect is taken into account. It is found that decaying solitary waves exist, in which the amplitude of the wave decreases exponentially as time increases. Meanwhile, the velocity of the solitary wave also slows down as time goes. This result implies that the damping coefficient is an important parameter in such a nonlinear system. Theoretical analysis has also been done by the reductive perturbation method. The result indicates that the nonlinear waves propagating in such a system can be described by the damped KdV equation. 相似文献
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数值研究了偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensate, BEC)在环形运动高斯势搅拌时的动力学行为.当高斯势运动速度和尺寸逐渐变化时,偶极BEC中将出现稳定层流、涡旋偶极子、Bénard–von Kármán(BvK)涡街以及混乱激发4种模式.结果表明高斯势在偶极BEC中圆周运动时产生涡街的条件非常苛刻,只有适当尺寸的高斯势以合适的速度运动时,尾流中周期性脱落的具有相同旋量的涡旋对稳定的分布在内外两个圆环上,形成BvK涡街.在实验参数下进行系统数值计算得到了不同偶极相互作用时的相图,讨论了偶极相互作用以及高斯势速度和尺寸对不同激发模式的影响.通过高斯势所受拖拽力的计算,分析了不同激发的物理学机制. 相似文献