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Showing 1 to 20 of 22 for “"KdV"”.
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Control and stabilization of kdv-kdv and kp type systems
… 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 Hirota-Satsuma system, we design feedback laws at the …
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The KdV and Whitham limit for a spatially periodic Boussinesq model
Wir betrachten die KdV-Approximation und die Whitham-Approximation für ein räumlich periodisches Boussinesq-Modell. Wir zeigen Abschätzungen der Differenz zwischen der KdV- beziehungsweise der Whitham-Approximation und echten Lösungen des ursprünglichen Modells, welche garantieren, dass diese …
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Asymptotic properties of solutions of a KdV-Burgers equation with localized dissipation
We study the Korteweg-de Vries-Burgers equation. With a deep investigation into the spectral and smoothing properties of the linearized system, it is shown by applying Banach Contraction Principle and Gronwall's Inequality to the integral equation based on the variation of parameters formula and …
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Numerical Search for a Phi4 Breather Mode and Study of the Phi4, Sine-Gordon, and Kdv Equations With Adiabatic Coefficients
Made available in DSpace on 2015-05-13T15:22:15Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 7913658.PDF: 4692069 bytes, checksum: faa1d0773e2caf5583528142c30a0dce (MD5) Previous issue date: 1978
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A study of certain multi-dimensional partial differential equations using Lie symmetry analysis
… Jimbo-Miwa equations, the combined KdV-negative-order KdV equation and the Calogero-Bogoyavlenskii-Schiff equation. Exact solutions of the (2 + 1)-dimensional and (3 + 1)-dimensional Boussinesq equations are obtained using the Lie symmetry method along with the simplest equation …
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Discrete Fourier restriction phenomenon associated with some periodic dispersive equations
… prove the local well-posedness of the periodic gKdV equations. The method we apply here is a generalization of Bourgain's ""denominator manipulation"". With this idea, we further discuss a more general type of KdV equation in Chapter 5. We establish the local well-posedness of the periodic KdV …
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Exact solutions and conservation laws of two-wave mode Kadomtsev-Petviashvili equation and a nonintegrable nonlinear equation
… equations namely the Korteweg-de Vries (KdV) equation as an illustrative example, nonintegrable nonlinear equation and two-wave mode Kadomtsev-Petviashvili (TKP) equation. We employ the multiplier method to find conservation laws. We also use Kudryashov and simplest equation methods to …
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Integrable Evolution Partial Differential Equations: Multidimensions and Dirichlet-to-Neumann Maps
… initial value problem of the Korteweg-de Vries (KdV) equation by what was later called the Inverse Scattering Transform. For some years the KdV equation with its striking properties was thought to be a unique case, until Zakharov and Shabat showed that the Nonlinear Schrödinger (NLS) equation can …
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Whitham Equations, Dispersionless KP Theory and Seiberg-Witten Variables
… of some Riemann Surfaces associated with the KdV equation. Briefly, a Riemann surface gives rise to integrable systems via the BA function. The averaging process gives modulation parameters Tn, ai and Whitham equations which describe the deformation of moduli such as branch points. We outline …
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Smoothing properties of certain dispersive nonlinear partial differential equations
… studies a periodic coupled Korteweg-de Vries (KdV) system. This system, known as the Majda-Biello system, displays an interesting dependancy on the coupling coefficient α linking the two KdV equations. Our main result is that the nonlinear part of the evolution resides in a smoother space for …
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Functional spaces : a direct approach
… structures (up to a certain order) of KdV equation and the Boussinesq equation. These are well known examples for nonlinear completely integrable evolution equations.
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Analysis and Implementation of High-Order Compact Finite Difference Schemes
… and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were combined with Euler and fourth-order Runge-Kutta time differencing. In most cases, the order of convergence of the numerical solution to the exact solution was the same as the formal order of …
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Self-similar singularity formation and wellposedness theory for compressible fluids and dispersive PDE
… 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 probabilistic setting.
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Stability of Periodic Waves in Nonlocal Dispersive Equations
… unidirectional Whitham and Korteweg-de Vries (KdV) equations.
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Nonsemilinear one-dimensional PDEs: analysis of PT deformed models and numerical study of compactons
… the complex PT-symmetric deformations of the KdV equation and of the inviscid Burgers equation, respectively. The second part of the thesis, comprising Chapters 3 and 4, contains a review and original numerical studies on the properties of certain quasilinear dispersive PDEs in one dimension …
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İkili ilaç etkin madde karışımlarının elektrokimyasal olarak incelenmesi
… türevi alınarak hesaplanmıştır. DPV ve KDV yöntemleri ile voltamogram oranları türev voltametrisine bağlı olarak ölçülen potansiyeller; sırasıyla levodopa-benserazid için 0,23 V ve 0,33 V; levodopa-karbidopa için 0,23 V ve 0,30 V; amilorid-hidroklorotiazid için 1,25 V ve 1,23 V ve KDV …
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A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves
… for the case (b₀,1) is coupled Schrödinger-KdV equations while it is a Schrödinger equation for another case (b,λ) â C₁. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is …
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Uncertainty quantification and prediction for non-autonomous linear and nonlinear systems
… we time-integrate the Korteweg-de Vries (KdV) equation with external stochastic forcing, comparing the performance of the DO and Monte Carlo schemes. We find that the DO scheme is computationally efficient to integrate uncertainty in such systems with external stochastic forcing.
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Wave breaking onset and dissipation in a fully non-linear, staggered grid Boussinesq model
… ☐ It is clear from prior results that linear, KdV or WNL models do not reproduce shoaling behavior for waves close to breaking. Although previous results (for example, Wei et al., 1995) have shown accurate results for FNL model shoaling of solitary waves, it is not a foregone conclusion that …
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Soliton solutions of noncommutative integrable systems
… historical attempts at finding solutions of the KdV equation, the Lax method and Hirota's direct method for finding multi-soliton solutions of an integrable system. Chapter 2 extends the ideas in Chapter 1 from equations of one spatial dimension to equations of two spatial dimensions, namely the …
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