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Showing 1 to 19 of 19 for “"Zakharov"”.
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The Initial Value Problem for the Zakharov System
The method of proof is an application of techniques developed by Bourgain and Kenig, Ponce and Vega. The equivalent fixed point problem is solved via the contraction principle in the $X\sb{s,b}$ spaces introduced by Bourgain. A detailed analysis of the nonlinear terms, exploiting the arithmetical …
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ΠΑΡΑΓΩΓΗ ΝΕΩΝ ΑΚΡΙΒΩΝ ΛΥΣΕΩΝ ΤΩΝ ΕΞΙΣΩΣΕΩΝ ΤΟΥ EINSTEIN ΜΕ ΤΗ ΜΕΘΟΔΟ ΤΗΣ ΑΝΤΙΣΤΡΟΦΗΣ ΣΚΕΔΑΣΗΣ ΤΩΝ BELINSKY-ZAKHAROV
THE INVERSE SCATTERING METHOD OF BELINSKY-ZAKHAROV (BZ) IS USED FOR THE CONSTRUCTION OF NEW EXACT SOLUTIONS OF THE EINSTEIN EQUATIONS. THIS METHOD IS APPLIED TO SPACETIMES POSSESING TWO COMMUTING (NON-NULL) KILLING VECTORS. THE BZ METHODIS PRESENTED IN A VERY USEFUL FORM IN THE CASE WHERE THE SEED …
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The interaction of shock waves and dispersive waves
… dispersive wave envelope. The system mimics the Zakharov equations from weak plasma turbulence theory but replaces the linear wave equation in that system by a nonlinear equation allowing shock formation. This nonlinear equation is a hyperbolic conservation law forced by the dispersive wave.
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Integrable Nonlinear Relativistic Equations
… Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to …
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A study of ocean wave statistical properties using nonlinear, directional, phase-resolved ocean wave-field simulations
… interactions based on the fully non-linear Zakharov equations. We vary the simulated wavefield's input spectral properties: directional spreading function, Phillips parameter and peak shape parameter. We then investigate the relationships between a wavefield's input spectral properties and …
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A study of ocean wave statistical properties using nonlinear, directional, phase-resolved ocean wave-field simulations
… interactions based on the fully non-linear Zakharov equations. We vary the simulated wavefield's input spectral properties: directional spreading function, Phillips parameter and peak shape parameter. We then investigate the relationships between a wavefield's input spectral properties and …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… equation in the nonrelativistic regime and the Zakharov system in the subsonic regime. Proofs of error estimate based on energy methods and cut-off techniques are presented, and numerical results are reported for verification purposes. Conservative schemes and schemes with uniform error bounds …
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Energy loss and equilibration of a highly energetic parton in QCD plasmas
… by a stationary solution known as the Kolmogorov-Zakharov spectrum, which is recovered at intermediate energy scales. This Kolmogorov-Zakharov spectrum leads to a scale invariant energy flux that we investigate in detail. Since the evolution is linear, the late time equilibration is studied using …
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Self-similar singularity formation and wellposedness theory for compressible fluids and dispersive PDE
… study of a different dispersive equation: the Zakharov– Kuznetsov equation. The equation is a generalization of the KdV equation to higher dimensions with applications in plasma physics. We improve the deterministic local wellposedness in the cyilnder both in the deterministic and the …
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Aspects of amplitudes, gravity & complexity
… gravitons to probe the so-called van Dam-Veltman-Zakharov (vDVZ) discontinuity in a purely on-shell manner, which we again find to be in agreement with the usual result. Additionally, we provide a clear physical picture as to the source of the discontinuity that is often obscured by the usual …
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Designing a Multichannel Sense-and-Avoid Radar for Small UASs
This thesis presents the design, analysis and test results of a 1.445 GHz Frequency-Modulated Continuous Wave (FMCW) collision-avoidance radar for Unmanned Aircraft Systems (UASs). This radar system is being developed by the department of Electrical Engineering (EE) in coordination with the …
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On Multi-component Nonlinear Schrödinger Equation with PT-Symmetry
… by using an appropriate modification of the Zakharov-Shabat dressing method. It is shown that the multi-component nonlinear Schrödinger equations of these types allow both regular and singular soliton configurations. Also, we show that the inverse scattering method can be viewed as a …
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The gravity of modern amplitudes: using on-shell scattering amplitudes to probe gravity
… supersymmetric version of the van Damme-Veltman-Zakharov (vDVZ) discontinuity. We construct the amplitudes of massive gravitinos (the superpartner of massive gravitons) and show that in the massless limit of the gravitinos there is the same discontinuity as found in massive gravity. This method …
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Smoothing properties of certain dispersive nonlinear partial differential equations
… is trivial. The next chapter studies the Zakharov and related Klein-Gordon-Schrödinger (KGS) systems on Euclidean spaces. Again, the main result is that the nonlinear part of the solution is smoother than the initial data. The proof relies on a new bilinear Bourgain-space estimate, which …
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Understanding of weak turbulence of capillary waves
First developed by Zakharov, Weak Turbulence Theory (WTT) aims at describing the steady-state statistical property of an ensemble of waves in weakly nonlinear interactions. In the wavenumber k domain, the WTT steady-state analytical solution yields a power-law inertial-range spectrum I - ka, with a …
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Light microscopy--a prototype for a remote image diagnosis system
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.
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Integrable Evolution Partial Differential Equations: Multidimensions and Dirichlet-to-Neumann Maps
… was thought to be a unique case, until Zakharov and Shabat showed that the Nonlinear Schrödinger (NLS) equation can also be solved using the same methodology. The KdV and NLS equations are integrable evolution equations in 1+1 dimensions (i.e., 1 spatial and 1 temporal dimension). There …
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On the Eigenvalues of the Manakov System
We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must …