Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Nixon, Sean D.
AU - Yang, Jianke
TI - Bifurcation of Soliton Families from Linear Modes in Non‐PT‐Symmetric Complex Potentials
JO - Studies in Applied Mathematics
PY - 2016-05-01T00:00:00///
VL - 136
IS - 4
SP - 459
EP - 483
N2 - Continuous families of solitons in the nonlinear SchrÃ¶dinger equation with non‐$\mathcal{PT}$‐symmetric
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 ${g}^{2}\left(x\right)+i{g}^{\prime}\left(x\right)$,
where $g\left(x\right)$
is an arbitrary real function. Using this constant of motion, the second‐order complex soliton equation is reduced to a new second‐order 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 non‐$\mathcal{PT}$‐symmetric
complex potentials. All analytical results are corroborated by numerical examples.
UR - https://www.ingentaconnect.com/content/bpl/sapm/2016/00000136/00000004/art00004
M3 - doi:10.1111/sapm.12117
UR - https://doi.org/10.1111/sapm.12117
ER -