Solutions Of Special Type Research Articles

SOLITONS AND DOMAIN-WALL-ARRAY SOLUTIONS OF THE SCHRÖDINGER FLOW AND LANDAU-LIFSHITZ EQUATION

We obtained some solitons and domain-wall-array solutions of the multidimensional Schrödinger flow and the Landau-Lifshitz equation using the homogeneous balance principle and general Jacobi elliptic-function method. These solutions include bright solitons and periodic solutions in terms of elliptic functions. We excluded several special types of solutions, such as kink profile solutions and dark solitons. The total phase profile of the solitons have two components: the kinematic origin, and the self-steepening effect. For the domain-wall-array solutions, the total phase profile consists of the kinematic origin, kinematic chirping, and self-steepening effect. In certain parameter domains, fundamental domain wall-array-solutions are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. For ODEs deduced from Schrödinger flow that have no analytical solution, phase analysis is used to identify and classify the typical evolutionary pattern. Furthermore, the existence of limit cycles is verified, and the locations of singularities are precisely estimated.

New impressive ideal optical soliton solutions to the space and time invariant nonlinear Schrödinger equation

• We will achieve new types of ideal optical soliton solution to the space and time invariant nonlinear Schrödinger equation. • The proposed model represents the two layer baroclinic instability and lossless symmetric two streams plasma instability. • Many types of special solutions in different forms as well as kink, anti-kink soliton solutions by using two powerful methods have been extracted. • The obtained results can be considered as benchmark to the results obtained by any numerical methods. In this paper, we will extract new types of ideal optical soliton solution to the space and time invariant nonlinear Schrödinger equation. The proposed model represents the two layer baroclinic instability and lossless symmetric two streams plasma instability. We will extract this Package of these ideal optical soliton solutions for this model by using two distinct methods one of them surrenders to the balance rule and has profile name the solitary wave ansatz method while the other doesn't surrender to the balance rule and has profile name the modified extended mapping method. The two suggested methods have been implemented in the same vein and parallel. Some of our achieved results agree with that realized previously by other authors in some cases and the remains are new.

التوثیق الفیلمی للمشروعات فی المملکة العربیة السعودیة باستخدام تقنیة الفاصل الزمنی وتطبیقات الرفع الفوری

ملخص تستعرض هذه الدراسة تقنية تصوير الفاصل الزمني بتقديمها أحد أهم الشرکات العالمية التي تقدم هذا النوع من التصوير باستخدام الکاميرات عالية الوضوح والدقة منذ العام 2006 حتى الآن ألا وهي شرکة EarthCam Inc, . وقد قام الباحث بهذا الأمر في ضوء أحد المشروعات السعودية التي تم استخدام هذا نظام هذه الشرکة بها وهو مشروع برج المملکة في مدينة جده. وقد اتبع الباحث منهج البحوث الوصفية حيث يستخدم هذا المنهج لوصف خصائص الظاهرة قيد الدراسة، والباحث هنا لم يجب على أسئلة حول کيف / متى / لماذا حدثت هذه الخصائص بل يعالج مسألة ماذا أو ما هي خصائص هذا البرنامج ومميزاته والسبب في ذلک هو أنه غالبا ما تسبق البحوث الوصفية البحوث التفسيرية. کما استخدمت هذه الدراسة اسلوب دراسة الحالة وتتمثل هنا في نظام Control 8 المستخدم من قبل شرکة EarthCam الامريکية حيث قام الباحث بتحليل متعمق قدر الامکان في خصائص هذا النظام ومميزاته. وفي جانب النتائج المستخلصة فإن هذه الدراسة تتبعت نتائج بحوث البرامج الحاسوبية والتي من ضمن أنواعها الحلول الخاصة، حيث قام الباحث بالتوصل لبعض نتائج وحلول إبداعية خاصة بمجال توثيق ومراقبة الإنشاءات العمرانية المترتبة على استخدام مثل هذه الکاميرات والتقنيات الحديثة الخاصة بالوسائط المتعددة. Abstract This study reviews the Time-lapse technology provided by one of the world's leading manufacturers of high definition and precision cameras from 2006 to date, EarthCam Inc. The researcher did this in the light of one of the Saudi projects that have been used this technology in “Kingdom Tower” project in Jeddah city. The researcher has followed the descriptive research approach. This method is used to describe the characteristics of the phenomenon under study, and the researcher here did not answer questions about how / when / why these characteristics occurred, but rather the question of what or what the characteristics of this program and its advantages. The study also used the case study method, which is the control 8 system which is invented by EarthCam USA, where the researcher analyzed as thoroughly as possible the characteristics of this system and its features. On the results side, this study followed the results of the research of the software programs, which are among the types of special solutions. The researcher reached some creative results and solutions for the field of documentation and control of the construction of the use of such cameras and modern technologies for multimedia.

Binary Darboux transformation and soliton solutions for the coupled complex modified Korteweg‐de Vries equations

This paper considers the coupled complex modified Korteweg‐de Vries (mKdV) equations and presents a binary Darboux transformation for the equations. As a direct application, we give a classification of general soliton solutions derived from vanishing and non‐vanishing backgrounds, on the basis of the dynamical behavior of the solutions. Special types of solutions in the presented solutions include breathers, bright‐bright solitons, bright‐dark solitons, bright‐W‐shaped solitons, and rogue wave solutions. Furthermore, dynamics and interactions of vector bright solitons are exhibited.

Vekua Systems in Hyperbolic Harmonic Analysis

In this paper we consider the solutions of the equation $${\mathcal {M}}_\kappa f=0$$ , where $${\mathcal {M}}_\kappa $$ is the so called modifier Dirac operator acting on functions $$f$$ defined in the upper half-space and taking values in the Clifford algebra. We look for solutions $$f(\underline{x},x_{n})$$ where the first variable is invariant under rotations. A special type of solution is generated by the so called spherical monogenic functions. These solutions may be characterize by a Vekua-type system and this system may be solved using Bessel functions. We will see that the solution of the equation $${\mathcal {M}}_\kappa f=0$$ in this case will be a product of Bessel functions.

On Vekua Systems and Their Connections to Hyperbolic Function Theory in the Plane

In this paper we study the solutions of the equation $$\Delta w- \frac{\alpha}{y}\partial_{y}w = 0,$$ where w is a complex valued function. This equation is related to the generalized axially symmetric potential theory which has been studied notably by Weinstein, see [12]. We have researched this equation earlier in higher dimensions in connection with the hyperbolic function theory. In this paper will see how this equation is related to the generalized analytic functions in the hyperbolic upper half-plane. We also study harmonic differential forms in the hyperbolic plane and using these we obtain special type of solutions for the preceding equation.

On other people’s terms: schools’ encounters with disabled students

According to Swedish legislation as well as laws pertaining to disabled citizens, Swedish schools are to be accessible for all children and adolescents. This implies that disabilities of any type must not be allowed to prevent students from completing their schooling on their own terms. The purpose of this research was to study the degree to which the Swedish school is accessible for all students. A total 200 professionals and politicians were interviewed alongside more than 30 upper secondary school students. The results show that the ambition level is high with regard to adapting educational programmes for the disabled student group, especially in the rhetoric of politicians and civil servants. However, in practice, teachers and head teachers have considerably more difficulty in delivering to students satisfactory schooling. This is often due to conflict between the striving for inclusion and the difficulty adapting learning environments during everyday classroom instruction. By use of institutional theory the study demonstrates that intentions as described of responsible politicians are altered in the system when confronted with the institutional reality. Schools’ meeting the natural variation of difference in the student group causes complications in educational work in which various solutions are attempted. When educational differentiation is found wanting in attempts to meet students’ various needs, various types of special solutions are sought, which have the objective of reducing heterogeneity among the students. This type of organisational differentiation seems accepted and legitimised where it concerns students having various kinds of school‐related difficulties, while seeming to create a disadvantage for some other students. One should understand this as thought coercion, where pressure from professionals in schools leaves little room for other strategies and in which the concept of the inclusive school is challenged.

Some special types of solutions of a class of the (N+1)-dimensional nonlinear wave equations

Some special types of solutions with arbitrary functions for the (N+1)-dimensional sine–cosine-Gordon equation, the (N+1)-dimensional double sinh-Gordon equation, and the (N+1)-dimensional sinh–cosinh-Gordon equations are constructed by means of the separation transformation approach. As an illustrative sample, the properties of some solutions are shown by their figures.

A note on a class of solitary-like solutions of the Tzitzéica equation generated by a similarity reduction

In this paper, new class of solutions of the Tzitzéica equation are derived by using the classical Lie symmetry analysis. The important aspect of this paper however is the fact that the analysis results in a new class of solitary-like solutions, the so-called cusp-solitary solutions. This special type of solutions are not found in the current literature and represents a necessary contribution for the whole solution manifold. The studied equation was originally found in the field of geometry, otherwise the Tzitzéica equation takes place in many branches of non-linear sciences. Therefore, explicit class of solutions connected by a physical meaning are of great importance. The analysis is restricted to the case of traveling waves represented by a similarity variable describing any wave propagation. A complete characterization of the group properties is given. The classical Lie point symmetries are derived and algebraic properties are determined. Similarity solutions and transformations are given in a most general form and have been derived for the first time in terms of Jacobian elliptic functions. It is worth to mention that the application of known powerful algebraic methods (e.g. special function transform methods) are not appropriate to study the solution manifold. Hence, the present paper is therefore suitable to create a deeper insight into the solution manifold with respect to the traveling wave picture.

A class of self-orthogonal 2-sequencings

Let 2K ndenote the complete multigraph on n vertices in which each edge has multiplicity two. If 2K ncan be partitioned into Hamiltonian paths such that any two distinct paths have exactly one edge in common, write 2K n→ P n. This paper considerably expands the set of known positive integers n such that 2K n→ P n. The solutions found have application to other similar problems. The basic idea is to consider an algebraic formulation of the problem in terms of 2-sequencings (terraces) with additional properties. Construction of these 2-sequencings gives a special type of solution for which very few examples have been known. The constructions detailed here hold eventually for certain classes of prime powers. For example, it is shown that there is a positive integer N such that if N < p n≡ 5 (mod 8) and 3 is not a fourth power residue of GF[p n], then the additive group of GF[p n] has a 2-sequencing of the required type—a self-orthogonal 2-sequencing. Some of the solutions admit a 2-coloring which is important for applications. The method of construction appears to be much better than the theoretical bounds that are obtained. The general bounds are found by means of a character sum argument.

Deforming some special solutions of the sine-Gordon equation to that of the double sine-Gordon equation

Some special types of solutions in the high dimensional sine-Gordon equation can be deformed to that of the double sine-Gordon equation by solving an ordinary differential equation or using a pure algebraic deformation relation.

Non-linear superposition in non-linear evolution equations

Special non-linear evolution equations are discussed and classified in integrable and non-integrable partial differential equations. Important methods of solution are sketched. An interesting task is the calculation of the so-called superposition functions permitting to construct from a few known solutions whole chains of further solutions. For integrable partial differential equations they are computed with the help of BAcklund transformations providing a rather general superposition rule for special types of solutions. At present however a consistent treatment of non-linear evolution equations is only possible in 1 + 1 space and time dimensions. The extension to higher space dimensions brings many problems. An insight into the results and problems in the one-dimensional case is given together with an outlook indicating the conceptual difficulties for a treatment in higher space dimensions.

Boundary problems and periodic Riccati equations

We consider the resolution problem of a periodic Riccati equation from the point of view of a generalized boundary problem that lets us reduce the differential problem to an algebraic equation of Riccati type. Sufficient conditions for the existence and calculus of special types of solutions are given.

Waves scattering by spherical inclusions in a solid host

A theoretical study is presented of the scattering of waves from a single spherical elastic inclusion embedded in an isotropic elastic medium. Three special types of solutions are obtained: scattering cross section, differential cross section and form function. Some solutions for absorbing media are included. Results indicate the various forms of expression of the solution are useful for different purposes.