Energy convergence for singular limits of Zakharov type systems
نویسندگان
چکیده
We prove existence and uniqueness of solutions to the Klein-Gordon-Zakharov system in the energy space H × L on some time interval which is uniform with respect to two large parameters c and α. These two parameter correspond to the plasma frequency and the sound speed. In the simultaneous high-frequency and subsonic limit, we recover the nonlinear Schrödinger system at the limit. We are also able to say more when we take the limits seperately.
منابع مشابه
Solitons And Periodic Solutions To The Generalized Zakharov-Kuznetsov Benjamin-Bona-Mahoney Equation
This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...
متن کاملConvergence of product integration method applied for numerical solution of linear weakly singular Volterra systems
We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.
متن کاملSemi-discretization in time for Nonlinear Zakharov Waves Equations
In this paper we construct and study discretizations of a nonlinear Zakharov-wave system occurring in plasma physics. These systems are generalizations of the Zakharov system that can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular limit process. One of the scheme is conservative but sensible to the polarization of the initial dat...
متن کاملA note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method
In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to nd the series solution of this equation via a reliable algorithm.
متن کاملNumerical Solution of Optimal Control of Time-varying Singular Systems via Operational Matrices
In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...
متن کامل