289 research outputs found
A multiple exp-function method for nonlinear differential equations and its application
A multiple exp-function method to exact multiple wave solutions of nonlinear
partial differential equations is proposed. The method is oriented towards ease
of use and capability of computer algebra systems, and provides a direct and
systematical solution procedure which generalizes Hirota's perturbation scheme.
With help of Maple, an application of the approach to the dimensional
potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and
2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton
type solutions. Two cases with specific values of the involved parameters are
plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure
High frequency integrable regimes in nonlocal nonlinear optics
We consider an integrable model which describes light beams propagating in
nonlocal nonlinear media of Cole-Cole type. The model is derived as high
frequency limit of both Maxwell equations and the nonlocal nonlinear
Schroedinger equation. We demonstrate that for a general form of nonlinearity
there exist selfguided light beams. In high frequency limit nonlocal
perturbations can be seen as a class of phase deformation along one direction.
We study in detail nonlocal perturbations described by the dispersionless
Veselov-Novikov (dVN) hierarchy. The dVN hierarchy is analyzed by the reduction
method based on symmetry constraints and by the quasiclassical Dbar-dressing
method. Quasiclassical Dbar-dressing method reveals a connection between
nonlocal nonlinear geometric optics and the theory of quasiconformal mappings
of the plane.Comment: 45 pages, 4 figure
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