scholarly journals On nonexistence of continuous families of stationary nonlinear modes for a class of complex potentials

2021 ◽  
Author(s):  
D. A. Zezyulin ◽  
A. O. Slobodyanyuk ◽  
G. L. Alfimov
Keyword(s):  
Complex Potentials ◽  
Nonlinear Modes

scholarly journals A universal form of localized complex potentials with spectral singularities

2020 ◽  
Vol 22 (1) ◽  
pp. 013057 ◽  
Author(s):  
Dmitry A Zezyulin ◽  
Vladimir V Konotop
Keyword(s):  
Complex Potentials ◽  
Universal Form ◽  
Spectral Singularities

An algorithm for solving the plane elastoplastic problem, based on use of the method of complex potentials and the method of conformal representations

1991 ◽  
Vol 23 (3) ◽  
pp. 285-289
Author(s):  
N. S. Mozharovskii ◽  
I. A. Bilyk ◽  
A. L. Shestopal
Keyword(s):  
Elastoplastic Problem ◽  
Complex Potentials

Nonlinear modes of an intense laser beam interacting with a periodic lattice of nanoparticle

2015 ◽  
Vol 22 (8) ◽  
pp. 082311 ◽  
Author(s):  
N. Sepehri Javan ◽  
S. H. H. Homami
Keyword(s):  
Laser Beam ◽  
Intense Laser ◽  
Periodic Lattice ◽  
Nonlinear Modes ◽  
Intense Laser Beam

Variational principle for vector spatial solitons and nonlinear modes

1991 ◽  
Vol 84 (5-6) ◽  
pp. 355-358
Author(s):  
Yijiang Chen
Keyword(s):  
Variational Principle ◽  
Spatial Solitons ◽  
Nonlinear Modes

scholarly journals Dominated Semigroups with Singular Complex Potentials

1997 ◽  
Vol 151 (2) ◽  
pp. 281-305 ◽  
Author(s):  
Vitali Liskevich ◽  
Amir Manavi
Keyword(s):  
Complex Potentials

scholarly journals Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials

2016 ◽  
Vol 94 (3) ◽  
Author(s):  
Franz G. Mertens ◽  
Fred Cooper ◽  
Edward Arévalo ◽  
Avinash Khare ◽  
Avadh Saxena ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Solitary Waves ◽  
Variational Approach ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Complex Potentials ◽  
Nonlinear Schrödinger

scholarly journals Vibration Analysis of a Nonlinear System With Cyclic Symmetry

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Aurélien Grolet ◽  
Fabrice Thouverez
Keyword(s):  
Nonlinear Differential Equations ◽  
Geometrical Nonlinearity ◽  
Harmonic Balance Method ◽  
Dynamic Responses ◽  
Cyclic Symmetry ◽  
Force Amplitude ◽  
Closed Curves ◽  
Nonlinear Modes ◽  
Nonlinear Localization ◽  
Engine Order

This work is devoted to the study of nonlinear dynamics of structures with cyclic symmetry under geometrical nonlinearity using the harmonic balance method (HBM). In order to study the influence of the nonlinearity due to large deflection of blades, a simplified model has been developed. It leads to nonlinear differential equations of the second order, linearly coupled, in which the nonlinearity appears by cubic terms. Periodic solutions in both free and forced cases are sought by the HBM coupled with an arc length continuation and stability analysis. In this study, specific attention has been paid to the evaluation of nonlinear modes and to the influence of excitation on dynamic responses. Indeed, several cases of excitation have been analyzed: punctual one and tuned or detuned low engine order. This paper shows that for a localized, or sufficiently detuned, excitation, several solutions can coexist, some of them being represented by closed curves in the frequency-amplitude domain. Those different kinds of solution meet up when increasing the force amplitude, leading to forced nonlinear localization. As the closed curves are not tied with the basic nonlinear solution, they are easily missed. They were calculated using a sequential continuation with the force amplitude as a parameter.

Evolution of vortex and quadrupole solitons in the complex potentials with saturable nonlinearity

2018 ◽  
Vol 20 (12) ◽  
pp. 125504 ◽  
Author(s):  
Hong Wang ◽  
Xiaoping Ren ◽  
Jing Huang ◽  
Yuanhang Weng
Keyword(s):  
Complex Potentials ◽  
Saturable Nonlinearity

Nonlinear modes in rotating double well potential with parity—time symmetry

2014 ◽  
Vol 23 (10) ◽  
pp. 104214 ◽  
Author(s):  
Wei Pang ◽  
Shen-He Fu ◽  
Jian-Xiong Wu ◽  
Yong-Yao Li ◽  
Zhi-Jie Mai
Keyword(s):  
Nonlinear Modes ◽  
Time Symmetry ◽  
Double Well Potential
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