Investigation of bright and dark solitons in α,β-Fermi Pasta Ulam lattice

• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（2）
• 所属期刊栏目: GENERAL
• 页码范围: 234-243
• 页数: 10页
• 语种: 英文
• DOI: 10.1088/1674-1056/abbbf3

摘要

We consider the Hamiltonian of α,β-Fermi Pasta Ulam lattice and explore the Hamilton-Jacobi formalism to ob-tain the discrete equation of motion.By using the continuum limit approximations and incorporating some normalized parameters,the extended Korteweg-de Vries equation is obtained,with solutions that elucidate on the Fermi Pasta Ulam paradox.We further derive the nonlinear Schrodinger amplitude equation from the extended Korteweg-de Vries equation,by exploring the reductive perturbative technique.The dispersion and nonlinear coefficients of this amplitude equation are functions of the α and β parameters,with the β parameter playing a crucial role in the modulational instability analysis of the system.For β greater than or equal to zero,no modulational instability is observed and only dark solitons are identified in the lattice.However for β less than zero,bright solitons are traced in the lattice for some large values of the wavenum-ber.Results of numerical simulations of both the Korteweg-de Vries and nonlinear Schr?dinger amplitude equations with periodic boundary conditions clearly show that the bright solitons conserve their amplitude and shape after collisions.