On Solitary-Wave Solutions for the Coupled Korteweg – de Vries and Modified Korteweg – de Vries Equations and their Dynamics

Analytic sech4-type traveling solitary-wave solutions of the coupled Korteweg-de Vries and modified Korteweg-de Vries equations proposed by Kersten-Krasil’shchik, are found by applying the auxiliary function method. The dynamical properties of the solitary-waves are studied by numerical simulations. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

Dynamics of Solitary-Waves in the Higher Order Korteweg –De Vries Equation Type (I)

We find new analytic solitary-wave solutions of the higher order wave equations of Korteweg - De Vries (KdV) type (I), using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves are stable for wide ranges of the model coefficients. We study the dynamics of the two solitary-waves by using the analytic solution as initial profiles and find that they interact elastically in the sense that the mass and energy of the system are conserved. This leads to the possibility of multi-soliton solutions of the higher order KdV type (I), which can not be found by current analytical methods. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

Dynamics of Solitary-waves in the Coupled Korteweg-De Vries Equations

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the coupled Korteweg-De Vries equation, using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves can be stable or unstable, depending on the coefficients of the model. We study the interaction dynamics by using the solitary-waves as initial profiles to show that the mass and energy of the coupled Korteweg- De Vries can be conserved for a negative third-order dispersion term. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

New Solitary-Wave Solutions for the Generalized Reaction Duffing Model and their Dynamics

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the generalized reaction Duffing model using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves can be stable or unstable depending on the coefficients of the model. We study the interaction dynamics by using the solitary-waves as initial profiles to show that the nonlinear terms may act as an effective driving force. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

Relativistic kinetic theory of electromagnetic waves in equilibrium magnetized plasma. General dispersion equations

The relativistic kinetic theory of parallel propagating electromagnetic waves in a magnetized equilibrium plasma is presented. On the basis of relativistic Vlasov–Maxwell equations, a general explicit dispersion relation is derived by a correct analytical continuation for all complex frequencies of electromagnetic waves.PACS Nos.: 52.25.Dg, 52.25.Xz, 52.27.Ep, 52.27.Ny, 52.35.Hr, 52.35.Mw, 52.35.Py

Dynamics of Combined Solitary-waves in the General Shallow Water Wave Models

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the general fifth-order shallow water wave models using the hyperbolic function ansatz method. We study the dynamical properties of the solutions in the combined form of a bright and a dark solitary-wave by using numerical simulations. It is shown that the solitary-waves can be stable or marginally stable, depending on the coefficients of the model.We study the interaction dynamics by using the combined solitary-waves as the initial profiles to show the formation of sech2-type solitary-waves in the presence of a strong nonlinear dispersion term. - PACS: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw