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Showing 1 to 7 of 7 for “"nonlinear klein gordon equation"”.
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ERROR ESTIMATES OF NUMERICAL METHODS FOR THE LONG-TIME DYNAMICS OF THE NONLINEAR KLEIN-GORDON EQUATION
… methods for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by $\varepsilon^2$ with $\varepsilon \in (0, 1]$ a dimensionless parameter.The analytical results indicate that the life-span of a smooth solution to this NKGE is …
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Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… oscillatory dispersive PDEs, including the nonlinear Klein-Gordon 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 …
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Coupled mode reductions and rotating wave approximations in nonlinear equations
… of coupled mode theory in the cubic-quintic nonlinear Schrodinger/Gross Pitaevskii (NLS/GP) equation with a linear double-well potential and study justifications of the rotating wave approximations in lattice systems. First, we study the long-time dynamics near a symmetry breaking bifurcation …
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Nonlinear dispersive equations with random initial data
… 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 regularity which …
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TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… study of global in time 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 …
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Stability of periodic solutions to nonlinear Klein-Gordon equations
… of periodic travelling wave solutions to nonlinear Klein-Gordon equations, subject to small and localized perturbations. Using the periodic Evans function technique, we analyze the spectrum of a linearized quadratic eigenvalue pencil associated with the linearized equation, in a …