scholarly journals Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach

2019 ◽  
Vol 118 ◽  
pp. 222-233 ◽  
Author(s):  
Yannis Kominis ◽  
Jesús Cuevas-Maraver ◽  
Panayotis G. Kevrekidis ◽  
Dimitrios J. Frantzeskakis ◽  
Anastasios Bountis
Keyword(s):  
Solitary Waves ◽  
Complex Potentials ◽  
Theory Approach ◽  
Symmetric Complex ◽  
Melnikov Theory

scholarly journals Parametric symmetries in exactly solvable real and PT symmetric complex potentials

2016 ◽  
Vol 57 (6) ◽  
pp. 062106 ◽  
Author(s):  
Rajesh Kumar Yadav ◽  
Avinash Khare ◽  
Bijan Bagchi ◽  
Nisha Kumari ◽  
Bhabani Prasad Mandal
Keyword(s):  
Complex Potentials ◽  
Exactly Solvable ◽  
Symmetric Complex

scholarly journals Scattering amplitudes for the rationally extended PT symmetric complex potentials

2016 ◽  
Vol 373 ◽  
pp. 163-177 ◽  
Author(s):  
Nisha Kumari ◽  
Rajesh Kumar Yadav ◽  
Avinash Khare ◽  
Bijan Bagchi ◽  
Bhabani Prasad Mandal
Keyword(s):  
Scattering Amplitudes ◽  
Complex Potentials ◽  
Symmetric Complex

scholarly journals Vector solitons in nonparity-time-symmetric complex potentials

2018 ◽  
Vol 26 (20) ◽  
pp. 26511 ◽  
Author(s):  
Xing Zhu ◽  
Yingji He
Keyword(s):  
Complex Potentials ◽  
Symmetric Complex

scholarly journals Supersymmetry of 𝒫𝒯-symmetric tridiagonal Hamiltonians

2021 ◽  
Author(s):  
Mohammad Walid AlMasri
Keyword(s):  
Energy Spectrum ◽  
Orthogonal Polynomials ◽  
Complex Potentials ◽  
Complex Conjugate ◽  
Matrix Elements ◽  
Morse Oscillator ◽  
Supersymmetric Partner ◽  
Natural Home ◽  
Symmetric Complex ◽  
Physical Quantities

We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian [Formula: see text] and its supersymmetric partner [Formula: see text] in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to [Formula: see text] can be recovered from those polynomials arising from the same problem for [Formula: see text] with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of [Formula: see text]-symmetric complex potentials. Finally, we solve the shifted [Formula: see text]-symmetric Morse oscillator exactly in the tridiagonal representation.

Solitons in Kerr media with two-dimensional non-parity-time-symmetric complex potentials

2021 ◽  
Vol 146 ◽  
pp. 110837
Author(s):  
Xing Zhu ◽  
Shangwen Liao ◽  
Zhen Cai ◽  
Yunli Qiu ◽  
Yingji He
Keyword(s):  
Complex Potentials ◽  
Two Dimensional ◽  
Kerr Media ◽  
Symmetric Complex

scholarly journals Nonlocal solitons supported by non-parity-time-symmetric complex potentials

2020 ◽  
Vol 22 (3) ◽  
pp. 033035
Author(s):  
Xing Zhu ◽  
Xi Peng ◽  
Yunli Qiu ◽  
Hongcheng Wang ◽  
Yingji He
Keyword(s):  
Complex Potentials ◽  
Symmetric Complex

scholarly journals COMPLEXIFIED PSUSY AND SSUSY INTERPRETATIONS OF SOME PT-SYMMETRIC HAMILTONIANS POSSESSING TWO SERIES OF REAL ENERGY EIGENVALUES

2002 ◽  
Vol 17 (01) ◽  
pp. 51-72 ◽  
Author(s):  
B. BAGCHI ◽  
S. MALLIK ◽  
C. QUESNE
Keyword(s):  
Harmonic Oscillator ◽  
Energy Levels ◽  
Double Series ◽  
Complex Potentials ◽  
Second Derivative ◽  
Energy Eigenvalues ◽  
Symmetric Complex

We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Pöschl–Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the fact that two superpotentials reside naturally in order-two parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes, we complexify their frameworks to successfully account for the three potentials.

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