Analytical solutions of the fifth-order time fractional nonlinear evolution equations by the unified method

This key purpose of this study is to investigate soliton solution of the fifth-order Sawada–Kotera and Caudrey–Dodd–Gibbon equations in the sense of time fractional local [Formula: see text]-derivatives. This important goal is achieved by employing the unified method. As a result, a number of dark and rational soliton solutions to the nonlinear model are retrieved. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behavior. The results demonstrate that the presented approach is more effective in solving issues in mathematical physics and other fields.

A Multitude of Languages - and One Country: Building up Communication among the Peoples of Russia through Translation

The article gives a survey of the problematics, historic and cultural practice of maintaining and developing the ethnic languages of Russia through translation; it retrospectively describes the history of polycultural co-existence (including the unified method of presentation for childrens folk lore in S. Marshaks version) and outlines the ways of dealing with todays urgent problems of preserving ethnic language. The article describes the models of reconstructing the lost texts and the strategies of translating the texts of small ethnic groups, as well as the models of maintaining the quality of translation from Russias ethnic languages into Russian. We especially stress the importance of the Russian language in its role of the cultural mediator. The article pays due attention to the need to develop specific practiceoriented theories of translation which would embrace the global experience in translatology and take into account the specificity of ethno-centric mentality and the ways to keep it in translation. The article is an introduction to the following materials in the volume.

Weighting with Life Cycle Assessment and Cradle to Cradle: A Methodology for Global Sustainability Design

Sustainable product design uses methodologies focused on eco-effectiveness and eco-efficiency for the proposal of innovative technological solutions and for the control of environmental impacts during the product life cycle. One of the main drawbacks of such techniques is their qualitative nature, associated with a decision-making process that is sometimes arbitrary, or with unverifiable data; this means that several complementary tools are currently being used to reduce the error in the results obtained. This situation makes the unification of procedures necessary. In this context, this research develops a methodology for the sustainable design of industrial products that integrates life cycle assessment (in its environmental, economic and social application) and cradle-to-cradle techniques. For this purpose, a new assessment process is proposed, based on damage, developing LCA+C2C endpoint indicators. The methodology is subsequently verified in a case study of products for sustainable mobility (city trike electric). The results show that an integrated LCA+C2C assessment can help to propose more balanced sustainable strategies and would be a suitable method to measure tradeoffs between economic, social and environmental results, for practical purposes and future redesigns. The unified method provides a procedure to design a solution with a trade-off between eco-efficient and eco-effective criteria; it also simplifies the design phases, facilitates the interpretation of the results and provides a quantitative scope to the cradle-to-cradle framework.

A Generalized Kundu-Eckhaus Equation With An Extra-Dispersion: Pulses Configuration

Raman effect is due to self-phase modulation (SPM), which is embedded in Kundu-Eckhaus equation KEE. Here, a generalized KEE is suggested by accounting for an extra dispersion. Here, we are concerned with finding the exact solutions of the proposed equation, which is done by using the unified method. In this work, we aim to show that the optical pulses OPs propagation in optical fibers may show a variety of shapes. Waves of multiple geometric shapes are observed. Among these waves, hybrid lumps, soliton, cascade, complex chirped, hybrid w-shaped, rhombus (diamond) waves and soliton modulation, which is induced by SPM. Further, the pulses intensity, frequency, wavelength, polarization, and spectral content are introduced. The results found here are of great interest in experimenting the effects of the induced dispersion on pulses configurations. Further, the colliding dynamics are inspected and as it is observed that no rogue or sharp waves formation holds, so the collision is elastic.

Chirped, breathers, diamond and W-shaped optical waves propagation in nonself-phase modulation medium. Biswas–Arshed equation

Self-phase modulation (SPM) induces a varying refractive index of the medium due to the optical Kerr effect. The optical waves propagation (OWP) in a medium with SPM occupied a remarkable area of research in the literature. A model equation to describe OWP in the absence of SPM was proposed very recently by Biswas–Arshed equation (BAE). This work is based on constructing the solutions that describe the waves which arise from soliton-periodic wave collisions. A variety of geometric optical wave structures are observed. Here, a transformation that allows to investigate the multi-geometric structures of OW’s result from soliton-periodic wave collisions is introduced. Chirped, conoidal, breathers, diamond and W-shaped optical waves are shown to propagate in the medium in the absence of SPM. The exact solutions of BAE are obtained by using the unified method, which was presented recently. We mention that the results found here, are completely new.

Construction of rogue waves and conservation laws of the complex coupled Kadomtsev–Petviashvili equation

In this work, the solutions of the real coupled Kadomtsev–Petviashvili equations (KPEs) are obtained and they are used to find the ones of the complex system. To this end, the extension theorem is used. The formation of rogue wave (RW) is shown to occur via inelastic collisions of lines-lump solitons and periodic waves and also of two elliptic waves. The quadratic invariant is used to show the phase portrait and bifurcation through the contour plot. Further, the conservation laws (CLs) are constructed by means of new conservation theorem by finding the governing system of equation. The results are given, work consolidated from a previous work, by the first two authors, for suggesting a mechanism for the formation of RW when the complex Korteweg–de Vries equation was studied. Based on the exact solutions found here, numerical computations are carried out and they are represented graphically. Finally, the unified method (UM) can be applied to solve a variety of partial differential equations in science and engineering.

Exact solutions of the cubic Boussinesq and the coupled Higgs system

We present explicit exact solutions of some evolution equations including cubic Boussinesq and coupled Higgs system by the unified method. The explicit solutions are expressed in terms of some elementary functions including trigonometric, exponential, and polynomial. The method is applied to a number of special test problems to test the strength of the method and computational results indicate the power and efficiency of the method.