scholarly journals Two-Dimensional Solitons and Vortices in Linear and Nonlinear Lattice Potentials

10.5772/66543 ◽  
2017 ◽  
Author(s):  
Jianhua Zeng ◽  
Boris A. Malomed
Keyword(s):  
Two Dimensional ◽  
Nonlinear Lattice ◽  
Linear And Nonlinear

scholarly journals Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves

2018 ◽  
Vol 52 (4) ◽  
pp. 1569-1596 ◽  
Author(s):  
Xavier Antoine ◽  
Fengji Hou ◽  
Emmanuel Lorin
Keyword(s):  
Domain Decomposition ◽  
Decomposition Methods ◽  
Nonlinear Schrödinger Equations ◽  
Waveform Relaxation ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Domain Decomposition Methods ◽  
Schwarz Waveform Relaxation ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear

This paper is devoted to the analysis of convergence of Schwarz Waveform Relaxation (SWR) domain decomposition methods (DDM) for solving the stationary linear and nonlinear Schrödinger equations by the imaginary-time method. Although SWR are extensively used for numerically solving high-dimensional quantum and classical wave equations, the analysis of convergence and of the rate of convergence is still largely open for linear equations with variable coefficients and nonlinear equations. The aim of this paper is to tackle this problem for both the linear and nonlinear Schrödinger equations in the two-dimensional setting. By extending ideas and concepts presented earlier [X. Antoine and E. Lorin, Numer. Math. 137 (2017) 923–958] and by using pseudodifferential calculus, we prove the convergence and determine some approximate rates of convergence of the two-dimensional Classical SWR method for two subdomains with smooth boundary. Some numerical experiments are also proposed to validate the analysis.

scholarly journals SCATTERING ANALYSIS FOR SHIP KELVIN WAKES ON TWO-DIMENSIONAL LINEAR AND NONLINEAR SEA SURFACES

2013 ◽  
Vol 52 ◽  
pp. 405-423
Author(s):  
Rong-Qing Sun ◽  
Min Zhang ◽  
Chao Wang ◽  
Xiao-Feng Yuan
Keyword(s):  
Two Dimensional ◽  
Linear And Nonlinear

The Nonlinear Optical Transition Bleaching in Tellurene

Nanoscale ◽  
2021 ◽  
Author(s):  
Yiduo Wang ◽  
Yingwei Wang ◽  
Yulan Dong ◽  
Li Zhou ◽  
Hao Wei ◽  
...  
Keyword(s):  
Optical Properties ◽  
Optical Anisotropy ◽  
Nonlinear Optical ◽  
Optical Transition ◽  
Nonlinear Optical Properties ◽  
Two Dimensional ◽  
Linear And Nonlinear

To date, outstanding linear and nonlinear optical properties of tellurene, caused by multiple two-dimensional (2D) phases and optical anisotropy, have been attracted considerable interest for potential nanophotonics applications. In this...

Linear and nonlinear electrical conduction in quasi-two-dimensional quantum wells

1987 ◽  
Vol 35 (3) ◽  
pp. 1334-1344 ◽  
Author(s):  
P. Vasilopoulos ◽  
M. Charbonneau ◽  
C. Van Vliet
Keyword(s):  
Quantum Wells ◽  
Electrical Conduction ◽  
Two Dimensional ◽  
Linear And Nonlinear

scholarly journals Linear and nonlinear discrete light propagation in weakly modulated large-area two-dimensional photonic lattice slab in LiNbO_3:Fe crystal

2009 ◽  
Vol 17 (25) ◽  
pp. 23078 ◽  
Author(s):  
Xinyuan Qi ◽  
Guoquan Zhang ◽  
Ningning Xu ◽  
Yiling Qi ◽  
Bin Han ◽  
...  
Keyword(s):  
Light Propagation ◽  
Two Dimensional ◽  
Large Area ◽  
Linear And Nonlinear

scholarly journals On Hokusai's Great wave off Kanagawa : localization, linearity and a rogue wave in sub-Antarctic waters

2013 ◽  
Vol 67 (2) ◽  
pp. 159-164 ◽  
Author(s):  
J. M. Dudley ◽  
V. Sarano ◽  
F. Dias
Keyword(s):  
Nonlinear Wave ◽  
Rogue Wave ◽  
Open Ocean ◽  
Two Dimensional ◽  
Wave Dynamics ◽  
Antarctic Waters ◽  
Storm Wave ◽  
Linear And Nonlinear

The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63 , 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave 's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave . In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.

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