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Showing 1 to 10 of 10 for “"Dispersive Equations"”.
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Nonlinear dispersive equations with random initial data
In the first part of this thesis we consider the defocusing nonlinear wave equation of power-type on R3. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of initial data of supercritical …
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Stability of Periodic Waves in Nonlocal Dispersive Equations
… the existence and stability of periodic waves in equations that possess nonlocal dispersion, i.e. equations in which the dispersion relation between the temporal frequency, omega, and wavenumber, k, of a plane wave is not polynomial in ik. In models that involve only classical derivative operators …
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The role of smoothing effect in some dispersive equations
… effect in the local well-posedness theory of dispersive partial differential equations in three different contexts. First, we use it to overcome a loss of derivatives in a family of nonlocal dispersive equations. Second, we exploit a discrete version of the smoothing effect to study a discrete …
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Numerical Methods and Their Analysis for Some Nonlinear Dispersive Equations
… to the numerical solutions of several classes of dispersive equations, namely, the coupled Schrodinger-Poisson (SP) type system, the Klein-Gordon (KG) equation, the sine-Gordon (SG) and perturbed Schrodinger (PNLS) equations. For SP type system, various numerical methods were compared for ground …
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On the Stability of Periodic Solutions of Nonlinear Dispersive Equations
… show how our results extend to other classes of dispersive equations. In particular, we derive modulational and finite-wavelength instability indices for the generalized Benjamin-Bona-Mahony (gBBM) equation, as well as the generalized Camassa-Holm equation. Moreover, we prove a transverse …
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Discrete Fourier restriction phenomenon associated with some periodic dispersive equations
… phenomenon associated with Schrodinger equations. We study the size of the Fourier transform of a periodic function on a truncated discrete paraboloid. We develop two ways to tackle the problem, and the second one recovers Bourgain's level set result on Strichartz estimates associated …
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Self-similar singularity formation and wellposedness theory for compressible fluids and dispersive PDE
… formation and local wellposedness of fluid equations and dispersive PDE. Regarding singularity formation, we construct radially symmetric smooth selfsimilar profiles for the compressible Euler equations which exhibit an implosion type singularity in finite time. This will be the first part …
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Smoothing properties of certain dispersive nonlinear partial differential equations
… concerned with the smoothing properties of dispersive equations and systems. Smoothing in this context means that the nonlinear part of the solution flow is of higher regularity than the initial data. We establish this property, and some of its consequences, for several equations. The first …
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Control and stabilization of kdv-kdv and kp type systems
… stabilization and control of several nonlinear dispersive systems, including the Boussinesq KdV-KdV type system, the Hirota-Satsuma system, the Kadomtsev-Petviashvili (KP) equation and its higher-order variant, the Kawahara-KP (K- KP) equation. For the Boussinesq KdV-KdV type system and …
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Stability bounds for nonlinear dispersive Hamiltonian partial differential equations
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms