The nonlinear Schrodinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations

被引：8

作者：

Yan, Zhenya ^{[1
]}

Chen, Yong

机构：

[1] Chinese Acad Sci, Inst Syst Sci, Key Lab Math Mechanizat, AMSS, Beijing 100190, Peoples R China

来源：

CHAOS | 2017年 / 27卷 / 07期

关键词：

LOCALIZED MODES; WAVE-GUIDES; FAMILIES; STABILITY; DYNAMICS; REAL;

D O I：

10.1063/1.4995363

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the nonlinear Schrodinger (NLS) equation with generalized nonlinearities and complex non-Hermitian potentials and present the novel parity-time-(PT-) symmetric potentials for the NLS equation with power-law nonlinearities supporting some bright solitons. For distinct types of PT-symmetric potentials including Scarf-II, Hermite-Gaussian, and asymptotically periodic potentials, we, respectively, explore the phase transitions for the linear Hamiltonian operators. Moreover, we analytically find stable bright solitons in the generalized NLS equations with several types of PT-symmetric potentials, and their stability is corroborated by the linear stability spectrum and direct wave-propagation simulations. Interactions of two solitons are also explored. More interestingly, we find that the nonlinearity can excite the unstable linear modes (i.e., possessing broken linear PT-symmetric phase) to stable nonlinear modes. The results may excite potential applications in nonlinear optics, Bose-Einstein condensates, and relevant fields. Published by AIP Publishing.

引用

页数：14

共 86 条

[1] Dissipative periodic waves, solitons, and breathers of the nonlinear Schrodinger equation with complex potentials [J].

Abdullaev, F. Kh. ;

Konotop, V. V. ;

Salerno, M. ;

Yulin, A. V. .

PHYSICAL REVIEW E, 2010, 82 (05)

[2] Solitons in PT-symmetric nonlinear lattices [J].

Abdullaev, Fatkhulla Kh. ;

Kartashov, Yaroslav V. ;

Konotop, Vladimir V. ;

Zezyulin, Dmitry A. .

PHYSICAL REVIEW A, 2011, 83 (04)

[3] Dark solitons and vortices in PT-symmetric nonlinear media: From spontaneous symmetry breaking to nonlinear PT phase transitions [J].

Achilleos, V. ;

Kevrekidis, P. G. ;

Frantzeskakis, D. J. ;

Carretero-Gonzalez, R. .

PHYSICAL REVIEW A, 2012, 86 (01)

[4] Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential [J].

Ahmed, Z .

PHYSICS LETTERS A, 2001, 282 (06) :343-348

[5] Optical solitons in PT-symmetric nonlinear couplers with gain and loss [J].

Alexeeva, N. V. ;

Barashenkov, I. V. ;

Sukhorukov, Andrey A. ;

Kivshar, Yuri S. .

PHYSICAL REVIEW A, 2012, 85 (06)

[6]

Bagarello F., 2016, NONHERMITIAN HAMILTO

[7] Generalized continuity equation and modified normalization in PT-symmetric quantum mechanics [J].

Bagchi, B ;

Quesne, C ;

Znojil, M .

MODERN PHYSICS LETTERS A, 2001, 16 (31) :2047-2057

[8] Making sense of non-Hermitian Hamiltonians [J].

Bender, Carl M. .

REPORTS ON PROGRESS IN PHYSICS, 2007, 70 (06) :947-1018

[9] Complex extension of quantum mechanics [J].

Bender, CM ;

Brody, DC ;

Jones, HF .

PHYSICAL REVIEW LETTERS, 2002, 89 (27)

[10] Real spectra in non-Hermitian Hamiltonians having PT symmetry [J].

Bender, CM ;

Boettcher, S .

PHYSICAL REVIEW LETTERS, 1998, 80 (24) :5243-5246

← 1 2 3 4 5 6 7 8 9 →