研究目的
To study the bifurcation diagrams organizing gap solitons in the semi-infinite gap of the continuous cubic-quintic Gross-Pitaevskii equation with a spatially periodic potential, focusing on the phenomena of forced snaking and foliated snaking, and to investigate the stability and dynamics of these solitons under perturbations.
研究成果
The study identifies two distinct bifurcation diagrams organizing gap solitons in the semi-infinite gap, characterized by standard snaking for small lattice spacing and foliated snaking for large spacing. It demonstrates that multisoliton solutions can be stabilized with sufficiently large spacing, quenching the interaction between solitons. The solitons are shown to unbind from the potential under large perturbations, with their dynamics and breakup investigated through numerical simulations. A strongly nonlinear theory is developed to describe the depinning dynamics, providing insights into the behavior of perturbed solitons.
研究不足
The study is limited to the semi-infinite gap of the Gross-Pitaevskii equation and does not explore gap solitons in higher gaps. The numerical simulations are conducted on periodic domains, which may not fully capture the behavior of solitons on unbounded domains. The strongly nonlinear theory provided captures key aspects of the depinning dynamics but may not account for all complexities of the soliton interactions and radiation losses.
1：Experimental Design and Method Selection:
The study employs numerical continuation and linear stability analysis to explore the bifurcation structure and stability of gap solitons in the cubic-quintic Gross-Pitaevskii equation with a periodic potential. Direct numerical simulations are used to investigate the dynamics of these solitons under perturbations.
2：Sample Selection and Data Sources:
The study focuses on solutions of the form A(x, t) = e^{-im0t}u(x) describing standing oscillations with a fixed spatial profile and a rotating phase, solving a nonlinear ordinary differential equation derived from the Gross-Pitaevskii equation.
3：List of Experimental Equipment and Materials:
Numerical simulations are performed using computational tools for solving differential equations and analyzing their solutions, including pseudo-spectral methods for stability calculations and split-step methods for time evolution simulations.
4：Experimental Procedures and Operational Workflow:
The methodology involves numerical continuation of solutions, linear stability analysis using Fourier pseudo-spectral methods, and time-stepping simulations with a split-step method to study the dynamics of perturbed solitons.
5：Data Analysis Methods:
The analysis includes computing the linear stability eigenvalues, tracking the center of mass of soliton solutions, and analyzing the energy and phase dynamics of perturbed solitons.
独家科研数据包，助您复现前沿成果，加速创新突破
获取完整内容
