962 research outputs found
New exact traveling wave solutions for the Klein–Gordon–Zakharov equations
AbstractBased on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the Klein–Gordon–Zakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for u and n, (d) the singular traveling wave solutions, (e) periodic traveling wave solutions of triangle function types, and solitary wave solutions of rational function types. We not only rederive all known solutions of the Klein–Gordon–Zakharov equations in a systematic way but also obtain several entirely new and more general solutions. The variety of structures of the exact solutions of the Klein–Gordon–Zakharov equations is illustrated
Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces
We apply a new general method of anholonomic frames with associated nonlinear
connection structure to construct new classes of exact solutions of
Einstein-Dirac equations in five dimensional (5D)gravity. Such solutions are
parametrized by off-diagonal metrics in coordinate (holonomic) bases, or,
equivalently, by diagonal metrics given with respect to some anholonomic frames
(pentads, or funfbiends, satisfing corresponding constraint relations). We
consider two possibilities of generalization of the Taub NUT metric in order to
obtain vacuum solutions of 5D Einsitein equations with effective
renormalization of constants having distinguished anisotropies on an angular
parameter or on extra dimension coordinate. The constructions are extended to
solutions describing self-consistent propagations of 3D Dirac wave packets in
5D anisotropic Taub NUT spacetimes. We show that such anisotropic
configurations of spinor matter can induce gravitational 3D solitons being
solutions of Kadomtsev-Petviashvili or of sine-Gordon equations.Comment: revtex, 16 pages, version 4, affiliation changed, accepted to CQ
The Application of Bifurcation Method to Klein-Gordon-Zakharov Equations
Bifurcation method of dynamical systems is employed to study the Klein-Gordon-Zakharov equations. Under some parameter conditions, some explicit expressions of solutions for the equation are obtained. These solutions contain solitary wave solutions, blow-up solutions, periodic solutions, periodic blow-up solutions and kink-shaped solutions. Key Words: Klein-Gordon-Zakharov equations; Exact solutions; Bifurcation metho
A New Six Point Finite Difference Scheme for Nonlinear Waves Interaction Model
In the paper, the coupled 1D Klein-Gordon-Zakharov system (KGZ-equations in short) is considered as the model equation for wave-wave interaction in ionic media. A finite difference scheme is derived for the model equations. A new six point scheme, which is equivalent to the multi-symplectic integrator, is derived. The numerical simulation is also presented for the model equations. Keywords: Coupled 1D Klein-Gordon-Zakharov system; Energy conservation; Six-point schem
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