# Numerical computation of solitons for optical systems

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 43, Issue: 1, page 173-208
- ISSN: 0764-583X

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topDi Menza, Laurent. "Numerical computation of solitons for optical systems." ESAIM: Mathematical Modelling and Numerical Analysis 43.1 (2008): 173-208. <http://eudml.org/doc/194443>.

@article{DiMenza2008,

abstract = {
In this paper, we present numerical methods
for the determination of solitons, that consist in spatially localized
stationary states of nonlinear scalar equations or coupled systems
arising in nonlinear optics.
We first use the well-known shooting method in order to find
excited states (characterized by the number k of nodes) for the
classical nonlinear Schrödinger equation. Asymptotics can then
be derived in the limits of either large k are large nonlinear
exponents σ.
In a second part, we compute solitons for a nonlinear
system governing the propagation of two coupled
waves in a quadratic media in any
spatial dimension, starting from one-dimensional states obtained
with a shooting method and considering the dimension as a
continuation parameter. Finally, we investigate the case of three wave
mixing, for which the shooting method is not relevant.
},

author = {Di Menza, Laurent},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Nonlinear optics; elliptic problems; stationary states; shooting method; continuation method.; nonlinear optics; continuation method; numerical examples; solitons; nonlinear Schrödinger equation},

language = {eng},

month = {12},

number = {1},

pages = {173-208},

publisher = {EDP Sciences},

title = {Numerical computation of solitons for optical systems},

url = {http://eudml.org/doc/194443},

volume = {43},

year = {2008},

}

TY - JOUR

AU - Di Menza, Laurent

TI - Numerical computation of solitons for optical systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/12//

PB - EDP Sciences

VL - 43

IS - 1

SP - 173

EP - 208

AB -
In this paper, we present numerical methods
for the determination of solitons, that consist in spatially localized
stationary states of nonlinear scalar equations or coupled systems
arising in nonlinear optics.
We first use the well-known shooting method in order to find
excited states (characterized by the number k of nodes) for the
classical nonlinear Schrödinger equation. Asymptotics can then
be derived in the limits of either large k are large nonlinear
exponents σ.
In a second part, we compute solitons for a nonlinear
system governing the propagation of two coupled
waves in a quadratic media in any
spatial dimension, starting from one-dimensional states obtained
with a shooting method and considering the dimension as a
continuation parameter. Finally, we investigate the case of three wave
mixing, for which the shooting method is not relevant.

LA - eng

KW - Nonlinear optics; elliptic problems; stationary states; shooting method; continuation method.; nonlinear optics; continuation method; numerical examples; solitons; nonlinear Schrödinger equation

UR - http://eudml.org/doc/194443

ER -

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