194 research outputs found
Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms
We present the fifth-order equation of the nonlinear Schrodinger hierarchy. This integrable partial differential ¨
equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use
Darboux transformations to derive exact expressions for the most representative soliton solutions. This set
includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures
composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard
nonlinear Schrodinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated ¨
flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons,
which cannot exist for the standard NLSE.The authors acknowledge the support of the Australian
Research Council (Discovery Project No. DP140100265).
N.A. and A.A. acknowledge support from the Volkswagen
Stiftung and A.C. acknowledges Endeavour Postgraduate
Award support
Solutions of the higher-order Manakov-type continuous and discrete equations
We derive exact and approximate localized solutions for the Manakov-type continuous and discrete equations. We establish the correspondence between the solutions of the coupled Ablowitz-Ladik equations and the solutions of the coupled higher-order Manakov equations.The authors acknowledge the support of the ARC (Discovery
Project DP140100265). N.A. and A.A. acknowledge the
support of the Volkswagen Stiftung, while A.C. is grateful for
support through an Endeavour Fellowship
Multisoliton complexes in a sea of radiation modes
We derive exact analytical solutions describing multi-soliton complexes and
their interactions on top of a multi-component background in media with
self-focusing or self-defocusing Kerr-like nonlinearities. These results are
illustrated by numerical examples which demonstrate soliton collisions and
field decomposition between localized and radiation modes.Comment: 7 pages, 7 figure
Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions
We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schrödinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions
Extended nonlinear Schroeodinger equation with higher-order odd and even terms and its rogue wave solutions
We consider an extended nonlinear Schroeodinger equation with higher-order odd (third order) and
even (fourth order) terms with variable coecients. The resulting equation has soliton solutions
and approximate rogue wave solutions. We present these solutions up to second order. Moreover,
specic constraints on the parameters of higher-order terms provide integrability of the resulting
equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota, and
Lakshmanan - Porsezian - Daniel (LPD) equations. The resulting integrable equation admits exact
rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue
waves solutions of the corresponding equations
Comparison of measured and predicted bandwidth of graded-index multimode fibres
Measurements of pulse spreading in three graded index fibers have been performed over an extensive range of wavelengths, including regions in which the index profiles become optimal and the bandwidths correspondingly high. The refractive index distributions and profile dispersion parameter have been measured and used in a ray-tracing algorithm in order to predict bandwidths. Comparison reveals that averaging processes on the index data are usually necessary to account for noncircularity of the fiber and small variations in the deduced profile caused by the wavelength dependence of the near-field intensity distribution. Results obtained by this means usually tend to slightly underestimate the true fiber bandwidth, while alpha-profile predictions always result in overestimates by about one order of magnitude. Remaining discrepancies between measured and predicted bandwidths are attributed to small variations of the index profiles along the fiber length
Surface modification of Co-doped ZnO nanocrystals and its effects on the magnetic properties
A series of chemically prepared Co2+-doped ZnO colloids has been surface modified either by
growing shells of ZnSe or by the in situ encapsulation in poly styrene . The surface modification
effects using these two distinct chemical strategies on the magnetic properties of the nanocrystals
were probed by electron paramagnetic resonance EPR . Structural characterization by means of
x-ray diffraction and transmission electron microscopy gave no evidence of second phase formation
within the detection limits of the used equipment. The EPR analysis was carried out by simulations
of the powderlike EPR spectra. The results confirm that in the core of these nanocrystals Co was
incorporated as Co2+, occupying the Zn2+ sites in the wurtzite structure of ZnO. Additionally we
identify two Co signals stemming from the nanocrystals’ shell. The performed surface modifications
clearly change the relative intensity of the EPR spectrum components, revealing the core and shell
signals
Conservation Laws and Integral Relations for the Boussinesq Equation
We are concerned with conservation laws and integral relations associated with rational solutions of the Boussinesq equation, a soliton equation solvable by inverse scattering, which was first introduced by Boussinesq in 1871. The rational solutions are logarithmic derivatives of a polynomial, are algebraically decaying, and have a similar appearance to rogue-wave solutions of the focusing nonlinear Schrödinger equation. For these rational solutions, the constants of motion associated with the conserved quantities are zero and they have some interesting integral relations, which depend on the total degree of the associated polynomial
The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach
A symplectic theory approach is devised for solving the problem of
algebraic-analytical construction of integral submanifold imbeddings for
integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on
canonically symplectic phase spaces
献辞
The ability to unveil growing rogue waves in the ocean is essential for safe marine travel in stormy conditions. This vital problem has not been adequately addressed so far. We show that the specific triangular spectra of rogue waves can be detected at early stages of their development in a chaotic wave field. Continuously measuring the spectra of various parts of the wave field allows us to find a rogue wave before the dangerous peak appears. This possibility of early detection is a necessary part of a rogue wave early-warning system.N.A. is a grateful recipient of the Alexander von Humboldt Prize.
He acknowledges a grant on Extreme Events from the Volkswagen
Foundation. J.M.S.C. acknowledges support from the Spanish
Ministerio de Ciencia e Innovación under contract FIS2009-09895.
A.A. and N.D. acknowledge the support of the Australian Research
Council (Discovery Project DP110102068)
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