Poisson structure on the phase space associated to the hamiltonian dynamics of coupled Korteweg- de Vries type equations
نویسندگان
چکیده
We present the hamiltonian structures for a wide class of coupled Korteweg-de Vries systems, including the Gear and Grimshaw system that models the strong interaction of internal waves in a stratified liquid and the system of Lou, Tong, Hu and Tang that describes a two layer fluid model. Among the hamiltonian structures of these systems we found new Poisson brackets which define consistent algebras of observables.
منابع مشابه
New analytical soliton type solutions for double layers structure model of extended KdV equation
In this present study the double layers structure model of extended Korteweg-de Vries(K-dV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma model. Then by using of new analytical method we obtain the new exact solitary wave solutions of this equation. Double layer is a structure in plasma and consists of two p...
متن کاملA Novel Approach for Korteweg-de Vries Equation of Fractional Order
In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very ef...
متن کاملAdomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation
Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle n...
متن کاملHamiltonian Structure and New Exact Soliton Solutions of Some Korteweg – De Vries Equations
In this paper, we discuss the Hamiltonian structure of Korteweg–de Vries equation, modified Korteweg–de Vries equation, and generalized Korteweg– de Vries equation. We proposed the Sine-function algorithm to obtain the exact solution for non-linear partial differential equations. This method is used to obtain the exact solutions for KdV, mKdV and GKdV equations. Also, we have applied the method...
متن کاملEnergy preserving integration of bi-Hamiltonian partial differential equations
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating ...
متن کامل