Analytical solutions for nonlinear systems using Nucci's reduction approach and generalized projective Riccati equations

In this study, the Nucci's reduction approach and the method of generalized projective Riccati equations (GPREs) were utilized to derive novel analytical solutions for the (1+1)-dimensional classical Boussinesq equations, the generalized reaction Duffing model, and the nonlinear Pochhammer-Chree equation. The nonlinear systems mentioned earlier have been solved using analytical methods, which impose certain limitations on the interaction parameters and the coefficients of the guess solutions. However, in the case of the double sub-equation guess solution, analytic solutions were allowed. The soliton solutions that were obtained through this method display real positive values for the wave phase transformation, which is a novel result in the application of the generalized projective Riccati method. In previous applications of this method, the real positive properties of the solutions were not thoroughly investigated

Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems

In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the family of the trial functions). Thus, the residual is calculated, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that only the parameter regimes for the existence of solitary waves had previously been analyzed for the microstructure PDE considered here, the results obtained here are both new and timely

The (

The two variable (G'/G,1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear evolution equations, namely, the nonlinear Klein-Gordon equations and the nonlinear Pochhammer-Chree equations. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations are rediscovered from the traveling waves. This method can be thought of as the generalization of well-known original (G'/G)-expansion method proposed by Wang et al. It is shown that the two variable (G'/G,1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics

Wave Propagation in Materials for Modern Applications

In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas

Damage modeling of carbon epoxy laminated composites submitted to impact loading

In the aerospace industry, composite structures design rules and admissible criteria are not well known for strength sustainability after impact induced damage. Predictive numerical tools are thought to be used to reduce design and certification time and costs, and to determine links between the inner behaviour of the material and the outer designable behaviour of structures. In this frame, it is aimed in this study to compare real tests damage measurements and two kinds of numerical damage predictions: one with geometrical openings for delamination discontinuity modelling, and one without any mesh opening that represents damage in a continuous way. Our attention is focused on two types of pre-impregnated unidirectional materials: T700/M21S and T800/M21S both strain rate sensitive because of a high percentage of thermoplastics in the M21 resin. Quasi-static and dynamic characterization tests have been carried out on balanced angle ply [±θ] laminates using Split Hopkinson's Pressure Bars. A saturation of through ply cracking has been outlined and strain rate effect on T800/M21S coupons' strength has been established up to medium strain rates. User defined cohesive finite elements are implemented in the non-linear explicit finite element analysis (FEA) code LS-DYNA® to model the dynamic delamination opening. At the same time a user defined deterministic continuous damage unidirectional composite material model is developed on the basis of the Matzenmiller-Lubliner-Taylor model widely used for woven composites. Initiation and growth of damage are predicted up to saturation and fracture for various pure and coupled damage mechanisms including delamination and matrix cracking, with criteria based on the experimental characterization. Impact induced damage from experimental measurements and numerical predictions are compared for T800/M21S aeronautical samples impacted at different energy levels. The effect on internal damage and residual indentations of 2 different masses and velocities has been evaluated. It is shown that the cohesive discontinuous delamination and the continuous damage coupling numerical models give both a good prediction of the global flexural behaviour of the structure. Spatial extension in shape and dimensions of damage through the plates' thickness is well predicted by the continuous model while the cohesive model is more diffusive leading to "isotropic" delamination predictions. Also, the continuous model gives better correlations between predicted and measured residual indentations after impact