Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

doi:10.1088/1674-1056/22/8/086302

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 86302-086302.doi: 10.1088/1674-1056/22/8/086302

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇下一篇

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

徐权^{a b}, 田强^b

a Department of Physics, Daqing Normal University, Daqing 163712, China;
b Department of Physics, Beijing Normal University, Beijing 100875, China

收稿日期:2012-12-20 修回日期:2013-01-29 出版日期:2013-06-27 发布日期:2013-06-27
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11247255) and the Natural Science Foundation of Heilongjiang Province, China (Grant No. A200506).

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

Xu Quan (徐权)^{a b}, Tian Qiang (田强)^b

a Department of Physics, Daqing Normal University, Daqing 163712, China;
b Department of Physics, Beijing Normal University, Beijing 100875, China

Received:2012-12-20 Revised:2013-01-29 Online:2013-06-27 Published:2013-06-27
Contact: Xu Quan E-mail:quanx2008@yeah.net
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11247255) and the Natural Science Foundation of Heilongjiang Province, China (Grant No. A200506).

摘要/Abstract

摘要： Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.

关键词: breather, quasiperiodic breather, chaotic breather

Abstract: Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.

Key words: breather, quasiperiodic breather, chaotic breather

中图分类号: (Anharmonic lattice modes)

63.20.Ry

63.20.Pw (Localized modes) 05.50.+q (Lattice theory and statistics)

徐权, 田强. Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice[J]. 中国物理B, 2013, 22(8): 86302-086302.

Xu Quan (徐权), Tian Qiang (田强). Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice[J]. Chin. Phys. B, 2013, 22(8): 86302-086302.

参考文献 20

[1]	Sievers A J and Takeno S 1998 Phys. Rev. Lett. 61 970
[2]	Cretegry T, Livi R and Spicci M 1998 Physica D 119 88
[3]	James G and Noble P 2004 Physica D 196 124
[4]	Hornguist M, Lennholm E and Basu C 2000 Physica D 136 88
[5]	Maniadis P, Zolotaryuk A V and Tsironis G P 2003 Phys. Rev. E 67 046612
[6]	James G and Kastner M 2007 Nonlinearity 20 631
[7]	Ullmann K, Lichtenberg A J and Corso G 2000 Phys. Rev. E 61 2471
[8]	Gershgorin B, Lvov Y V and Cai D 2005 Phys. Rev. Lett. 95 264302
[9]	Reigada R, Sarmiento A and Lindenberg K 2002 Phys. Rev. E 66 046607
[10]	Khomeriki R 2002 Phys. Rev. E 65 026605
[11]	Sanchez-Rey B, James G, Uevas J C and Archilla J F R 2004 Phys. Rev. B 70 014301
[12]	Johansson M and Aubry S 1997 Nonlinearity 10 1151
[13]	Cretegny T, Dauxois T, Ruffo S and Torcini A 1998 Physica D 121 109
[14]	Chechin G M, Dzhelauhova G S and Mehonoshina E A 2006 Phys. Rev. E 74 036608
[15]	Antonopoulos C and Bountis T 2006 Phys. Rev. E 73 056206
[16]	Hennig D 1999 Phys. Rev. E 59 1637
[17]	Maniadis P and Bountis T 2006 Phys. Rev. E 73 046211
[18]	Butt I A and Wattis J A D 2006 J. Phys. A: Math. Gen. 39 4955
[19]	Xu Q and Tian Q 2009 Chin. Phys. B 18 259
[20]	Xu Q and Tian Q 2007 Chin. Phys. Lett. 24 3347

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 20

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Feng Yuan(袁丰) and Behzad Ghanbari. Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations[J]. 中国物理B, 2023, 32(4): 40201-040201.
[2]	Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505.
[3]	Jing Wang(王静), Xue-Li Ding(丁学利), and Biao Li(李彪). Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation[J]. 中国物理B, 2022, 31(10): 100502-100502.
[4]	Jun-Cai Pu(蒲俊才), Jun Li(李军), and Yong Chen(陈勇). Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints[J]. 中国物理B, 2021, 30(6): 60202-060202.
[5]	Xiao-Min Wang(王晓敏) and Peng-Fei Li(李鹏飞). Breathers and solitons for the coupled nonlinear Schrödinger system in three-spine α-helical protein[J]. 中国物理B, 2021, 30(10): 100509-100509.
[6]	Zai-Dong Li(李再东), Qi-Qi Guo(郭奇奇), Yong Guo(郭永), Peng-Bin He(贺鹏斌), and Wu-Ming Liu(刘伍明). Interaction region of magnon-mediated spin torques and novel magnetic states[J]. 中国物理B, 2021, 30(10): 107506-107506.
[7]	杜仲, 田播, 屈启兴, 赵学慧. Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber[J]. 中国物理B, 2020, 29(3): 30202-030202.
[8]	李再东, 王洋洋, 贺鹏斌. Formation mechanism of asymmetric breather and rogue waves in pair-transition-coupled nonlinear Schrödinger equations[J]. 中国物理B, 2019, 28(1): 10504-010504.
[9]	苏琬涵, 谢家玉, 吴天乐, 唐炳. Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field[J]. 中国物理B, 2018, 27(9): 97501-097501.
[10]	任杨, 杨战营, 刘冲, 杨文力. Controllable optical superregular breathers in the femtosecond regime[J]. 中国物理B, 2018, 27(1): 10504-010504.
[11]	徐涛, 陈勇, 林机. Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics[J]. 中国物理B, 2017, 26(12): 120201-120201.
[12]	李再东, 吴璇, 李秋艳, 贺鹏斌. Kuznetsov-Ma soliton and Akhmediev breather of higher-order nonlinear Schrödinger equation[J]. 中国物理B, 2016, 25(1): 10507-010507.
[13]	冀慎统, 颜培根, 刘学深. Soliton breathers in spin-1 Bose–Einstein condensates[J]. 中国物理B, 2014, 23(3): 30311-030311.
[14]	Mirabeau Saha, Timoléon C. Kofané. Transcription’s bubble under the influence of long-range interactions and helicoidal coupling[J]. 中国物理B, 2013, 22(12): 129402-129402.
[15]	白志勇, 邓冬梅, 郭旗. Elegant Ince–Gaussian breathers in strongly nonlocal nonlinear media[J]. 中国物理B, 2012, 21(6): 64218-064218.