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Showing 1 to 11 of 11 for “"NLS equation"”.
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Maxwell-Bloch and nonlinear Schrodinger systems with nonzero background
… study of two main types of nonlinear evolution equations of physical signif-icance: (i) Maxwell-Bloch (MB) systems and (ii) nonlinear Schr ̈odinger (NLS) type. Maxwell-Bloch systems characterize the nonlinear resonant interactions between coherent light and an active optical medium [10, 18]. …
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Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses
… is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the …
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Analysis of solitary waves in inhomogeneous systems
… solitary waves of three nonlinear Schrödinger (NLS)-type models, namely, the NLS equation with an asymmetric double Dirac delta potential, the NLS equation with a Dirac delta potential on star graphs, and the discrete nonlinear Schrödinger (DNLS) equation. For the first model, we obtain analytic …
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Justification of a nonlinear Schrödinger model for polymers
<p>A model with nonlinear Schrödinger (NLS) equation used for describing pulse propagations in photopolymers is considered. We focus on a case in which change of refractive index is proportional to the square of amplitude of the electric field and consider 2-dimensional spatial domain. After formal …
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Integrable Evolution Partial Differential Equations: Multidimensions and Dirichlet-to-Neumann Maps
… thesis is about integrable Partial Differential Equations (PDEs). Here "integrable" means that the given PDE or system of PDEs can be written as the compatibility condition of a set of linear equations, the so-called Lax pair, and can be solved via a method related to the Inverse Scattering …
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
… of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a quantitative estimate on the low-to high frequency cascade which can occur due to the nonlinear evolution. In our work, we present two possible …
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The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation.
… of a study of the complex Ginzburg-Landau equation (CGL) as a perturbation of the nonlinear Schrodinger equation (NLS) in one dimension under periodic boundary conditions. Using an averaging technique which is similar to a Melnikov method for pde's, necessary conditions are derived for the …
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Dynamics and stability of gravity-capillary solitary waves
… to predictions of the nonlinear Schrbdinger (NLS) equation, some free solitary wave types are found to be unstable owing to exponentially effects terms that lie beyond standard two-scale perturba- tion theory. Moreover, numerical simulations show that unstable gravity-capillary solitary waves …
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Continuous and quad-graph integrable models with a boundary: Reflection maps and 3D-boundary consistency
… we consider the vector nonlinear Schrodinger (NLS) equation on the halfline. Using a Backlund transformation method which explores the folding symmetry of the system, classes of integrable boundary conditions (BCs) are derived. These BCs coincide with the linearizable BCs obtained using the …
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Solitons,spatiotemporal choas and synchronization in arrays of damped driven nonlinear oscillators
… amplitudes of the pendulums satisfy a system of equations in slow time, the "nonlinear Schrodinger (NLS) oscillators". The evolution of the chain of NLS oscillators is simulated numerically. Simulating the homogeneous chain, we demonstrate the existence of periodically oscillating solitons, the …
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TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… approximation for two nonlinear Schrödinger equations. Chapter 1 focuses on the non-relativistic limit of the one-dimensional cubic nonlinear Klein-Gordon equation, which is known (formally) to converge to the cubic nonlinear Schrödinger equation as c → ∞. More precisely, it is known that …