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 ...

By means of the modified CK’s direct method, we give out the relationship between variable coefficients of the fifth-order KdV equation and the corresponding constant coefficient ones. At the same time, we have studied the generalized fifth-order KdV equation with constants coefficients using the Lie symmetry group methods. By applying the nonclassical symmetry method we found that the analyzed...

In this paper we establish the nonlinear stability of solitary traveling-wave solutions for the Kawahara-KdV equation ut + uux + uxxx − γ1uxxxxx = 0, and the modified Kawahara-KdV equation ut + 3u 2ux + uxxx − γ2uxxxxx = 0, where γi ∈ R is a positive number when i = 1, 2. The main approach used to determine the stability of solitary traveling-waves will be the theory developed by Albert in [1].

We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. It is shown that two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the propo...

Cellulosic Ž bers have been used as cost-cutting Ž llers in plastic industry. Among the various factors, the Ž nal performance of the composite materials depends to a large extent on the adhesion between the polymer matrix and the reinforcement and therefore on the quality of the interface. To achieve optimum performance of the end product, sufŽ cient interaction between the matrix resin and th...

When applied to discriminant analysis (DA) biplot methodology leads to useful graphical displays for describing and quantifying multidimensional separation and overlap among classes. The principles of ordinary scatterplots are extended in these plots by adding information of all variables on the plot. However, we show that there are fundamental di¤erences between two-class DA problems and the c...

The fundamental frequency of a rectangular orthotropic plate having an arbitrary thickness variation is computed by using the method of Modi ed Vibrational Mode (MVM) shapes. The change of thickness within a plate is characterized by introducing a tapering index. It is shown that the vibrational mode shapes of a tapered plate is in fact a linear combination of various mode shapes of intact plat...

This paper presents a new numerical method for solving the population balance equation using the modi ed method of characteristics. Aggregation and break-up are neglected but the density function variations in the three-dimensional space and its dependence on the external elds are accounted for. The method is an interpretation of the Lagrangian approach. Based on a pre-speci ed grid, it follows...

The Thomas-Fermi (TF) equation has proved to beuseful for the treatment of many physical phenomena. In this pa-per, the traveling wave solutions of the KdV equation is investi-gated by the simplest equation method. Also, the effect of differentparameters on these solitary waves is considered. The numericalresults is conformed the good accuracy of presented method.