@article {Nixon:2016:0022-2526:459,
title = "Bifurcation of Soliton Families from Linear Modes in NonPTSymmetric Complex Potentials",
journal = "Studies in Applied Mathematics",
parent_itemid = "infobike://bpl/sapm",
publishercode ="bp",
year = "2016",
volume = "136",
number = "4",
publication date ="2016-05-01T00:00:00",
pages = "459-483",
itemtype = "ARTICLE",
issn = "0022-2526",
eissn = "1467-9590",
url = "https://www.ingentaconnect.com/content/bpl/sapm/2016/00000136/00000004/art00004",
doi = "doi:10.1111/sapm.12117",
author = "Nixon, Sean D. and Yang, Jianke",
abstract = "Continuous families of solitons in the nonlinear Schr{\"o}dinger equation with nonPTsymmetric
complex potentials and general forms of nonlinearity are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant of motion if and only if the complex potential is of a special form <math xmlns="http://www.w3.org/1998/Math/MathML"
display="inline" altimg="urn:x-wiley:00222526:media:sapm12117:sapm12117-math-0004" location="equation/sapm12117-math-0004.png">g2(x)+ig(x),
where g(x)
is an arbitrary real function. Using this constant of motion, the secondorder complex soliton equation is reduced to a new secondorder real equation for the amplitude of the soliton. From this real soliton equation, a novel perturbation technique is employed to show that continuous
families of solitons bifurcate out from linear discrete modes in these nonPTsymmetric
complex potentials. All analytical results are corroborated by numerical examples.",
}