Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

Journal Article · Sat Jul 15 04:00:00 EDT 2006 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776106070144· OSTI ID:21067667

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schroedinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schroedinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component 'bullets' having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized 'lump' solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.

• OSTI ID: 21067667
• Journal Information: Journal of Experimental and Theoretical Physics, Journal Name: Journal of Experimental and Theoretical Physics Journal Issue: 1 Vol. 103; ISSN JTPHES; ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
DIFFRACTION
EIKONAL APPROXIMATION
FUNCTIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PERTURBATION THEORY
SCHROEDINGER EQUATION
SOLITONS
THREE-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
WAVELENGTHS