228 research outputs found
Rogue waves of the Fokas-Lenells equation
The Fokas-Lenells (FL) equation arises as a model eqution which describes for
nonlinear pulse propagation in optical fibers by retaining terms up to the next
leading asymptotic order (in the leading asymptotic order the nonlinear
Schr\"odinger (NLS) equation results). Here we present an explicit analytical
representation for the rogue waves of the FL equation. This representation is
constructed by deriving an appropriate Darboux transformation (DT) and
utilizing a Taylor series expansion of the associated breather solution. when
certain higher-order nonlinear effects are considered, the propagation of rogue
waves in optical fibers is given.Comment: 7 pages, 3 figure
The hierarchy of higher order solutions of the derivative nonlinear Schr\"odinger equation
In this paper, we provide a simple method to generate higher order position
solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger
equation. The formulae of these higher order solutions are given in terms of
determinants. The dynamics and structures of solutions generated by this method
are studied
The higher order Rogue Wave solutions of the Gerdjikov-Ivanov equation
We construct higher order rogue wave solutions for the Gerdjikov-Ivanov
equation explicitly in term of determinant expression. Dynamics of both soliton
and non-soliton solutions is discussed. A family of solutions with distinct
structures are presented, which are new to the Gerdjikov-Ivanov equation
The Rogue Wave and breather solution of the Gerdjikov-Ivanov equation
The Gerdjikov-Ivanov (GI) system of and is defined by a quadratic
polynomial spectral problem with matrix coefficients. Each element
of the matrix of n-fold Darboux transformation of this system is expressed by a
ratio of determinant and determinant of
eigenfunctions, which implies the determinant representation of and
generated from known solution and . By choosing some special
eigenvalues and eigenfunctions according to the reduction conditions
, the determinant representation of provides
some new solutions of the GI equation. As examples, the breather solutions and
rogue wave of the GI is given explicitly by two-fold DT from a periodic "seed"
with a constant amplitude.Comment: 8 figures, 17 page
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