Новые поступления

On Solutions of Nonlinear Functional Differential Equations solutions of differential equations in nonlinear water waves
Nonlinear difference equations of order greater than one are of paramount importance in applications. Such equations appear naturally as a discrete analogues and as numerical solutions of differential equations and delay differential equations. They have models in various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our goal in this thesis is understanding the dynamics of nonlinear difference equations to construct the basic theory of this ?led. We believe that the results of this thesis are prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. Now we are going to give some examples for applications of difference equations.
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Nonlinear Fractional Order Differential Equations solutions of differential equations in nonlinear water waves
The main purpose of this work is to study the fractional order linear and nonlinear differential equations. This book is to present the analytical solutions of fractional order differential equations. The book is divided into two main parts: (a) - The fractional order ordinary and (b) - The fractional order partial differential equations. The aim of presenting, in a systematic manner, results including the solutions of linear and nonlinear system of fractional order equations arising in chemical kinetics by homotopy and variational methods, fractional order Riccati differential equations by less computational homotopy approach, explicit solutions of linear and nonlinear system of fractional order differential equations, nonlinear fractional order Swift–Hohenberg (S-H) equation, the fractional order Burgers equations and the time-fractional reaction-diffusion equations. The non-perturbative and numerical methods have been implemented to obtain the solutions of considered problems. Results will be developed which are useful for the researchers and it is also useful which will interact to its practical applications with engineers and mathematician.
6390 RUR
Solutions of Differential Equations in Nonlinear Water Waves solutions of differential equations in nonlinear water waves
This book is concerned with the study of nonlinear water waves, which is one of the important observable phenomena in Nature. This study is related to the fluid dynamics, in general, and to the oceans dynamics in particular. The solutions of nonlinear PDEs with constant and variable coefficients, which describe the wave motion of undulant bores in shallow water, are investigated by using various analytical methods to illustrate the relation between solitary and water waves. The important ideas and results for nonlinear dispersive properties and solitons, which originated from the investigations of water waves, are discussed. The stability analysis for the second order system of PDEs is studied by using the phase plane method. In addition, we use perturbation methods to study the water wave problems for an incompressible fluid under the acceleration gravity and surface tension. The conservation laws of some PDEs are established. We illustrate the resulting solutions in several 3D-graphics showing the shock and solitary wave nature in the flow. This book contains many concepts of water wave motion and different mathematical methods that help researchers in the relevant topics.
5490 RUR
Periodic solutions of a certain non-linear differential equations solutions of differential equations in nonlinear water waves
The study of nonlinear oscillators equations is of great importance not only in all areas of physics but also in engineering and other disciplines, since most phenomena in our word are nonlinear and are described by nonlinear equations. Recently, considerable attention has been direct towards the analytical solutions for nonlinear oscillators, for example, elliptic homotopy averaging method, amplitude-frequency formulation, homotopy perturbation method, parameter-expanding method, energy balance method, and others. The aim of this thesis is to study the periodic solutions for some physical systems which the mathematical formulation of these systems leads to a certain set of nonlinear ordinary differential equations of the second order.
5790 RUR
A Method for Solve the Nonlinear Fractional Differential Equations solutions of differential equations in nonlinear water waves
In this book is presented a new method introduced in order to establish solutions for fractional differential equations. This method is based on a combination of Adomian decomposition method and Laplace transform method. This new method can be applied to linear and nonlinear fractional differential equations. The method is illustrated on a series of examples including ordinary differential equations and systems of differential equations, partial differential equations and systems. The method can be used with the aid of symbolic calculus. For this reason we are suggested some Maple and Mathematica solutions of the examples investigated.
3939 RUR
Solutions of Nonlinear Parabolic Differential Equations solutions of differential equations in nonlinear water waves
In this book, solutions of nonlinear parabolic differential equations are investigated. More specifically, existence and non-existence theorems of solutions are presented. The first part involves the related results for the Cauchy problem for a set of nonlinear parabolic differential equations with critical exponent. Then the necessary and sufficient conditions are determined for the non-existence results of solutions for the corresponding Dirichlet and mixed boundary value problems. The proofs make use of the dilation and comparison arguments. Moreover, to generalize these results, proofs are given in n-dimension and for general type of domains. Finally, numerical simulations are also provided to verify the theoretical analysis
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Existence and stability of solutions to nonlinear dynamical systems solutions of differential equations in nonlinear water waves
This book is an outgrowth of our results on the existence and stability of solutions to nonlinear dynamical systems, stochastic systems, and impulsive systems over the last five years. In particular, we present the Razumikhin-type exponential stability criteria for impulsive stochastic functional differential systems, the stability analysis of neutral stochastic delay differential equations by a generalization of Banachs contraction principle and the globally asymptotical stability in the mean square for stochastic neural networks with time-varying delays and fixed moments of impulsive effect. Also, we discuss oscillation criteria based on a new weighted function for linear matrix Hamiltonian systems and the existences of the positive solutions or nontrivial solutions of nonlinear differential equations.
5790 RUR
Numerical Solutions of Algebraic, Differential and Integral Equations solutions of differential equations in nonlinear water waves
Designed for advanced undergraduate and graduate students in applied mathematics as well as researchers, this illuminating resource will introduce the reader to the fundamental aspects of three powerful iterative methods for handling equations with distinct structures. The book will serve nicely as a supplementary textbook for course study. The aim of this textbook is threefold: firstly, give a detailed review of the Adomian Decomposition Method for solving linear/nonlinear ordinary and partial differential equations, algebraic equations, delay differential equations, linear and nonlinear integral equations, and integro-differential equations. Secondly, the essential features of the He’s Variational Iteration Method are rigorously presented for solving a wide spectrum of equations. Finally, introduce a novel method based on manipulating Green’s functions and some popular fixed point iterations schemes, such as Picard's and Mann's, for the numerical solution of boundary value problems.
6890 RUR
On Some Asymptotic Solutions of Critically Damped Nonlinear Systems solutions of differential equations in nonlinear water waves
The study of nonlinear problems is of crucial in the areas of Applied Mathematics, Physics and Engineering, as well as other disciplines. The differential equations are linear or nonlinear, autonomous or non-autonomous. Practically, numerous differential equations involving physical phenomena are nonlinear. Methods of solutions of linear differential equations are comparatively easy and highly developed. Whereas, very little of a general character is known about nonlinear equations. An important approach to the study of such nonlinear oscillations is the small parameter expansion of Krylov-Bogoliubov-Mitropolski (KBM). This book is concerned the critically damped nonlinear systems by use of the KBM method. The presentation of this book is easy and intelligible by the beginners. Researchers who thoroughly cover the book will be well prepared to make important contributions to analyze nonlinear systems. It will be helpful in the area of mechanics, physics, engineering etc. The book contains a wide bibliography.
4839 RUR
Nonlinear Euler-Poisson-Darboux Equations solutions of differential equations in nonlinear water waves
This book is devoted to study multidimensional linear and nonlinear partial differential equations. Among several methods to deal with higher dimensional linear partial differential equations, the elegant method of Spherical Means has spacial importance since this method reduces the higher dimensional equations to the one dimensional radial equations of Euler-Poisson-Darboux type which are well studied. Although this method is applicable only to the linear differential equations, by some special transformations, like the Cole-Hopf transformation and the Backlaund transformation, exact solutions of multidimensional nonlinear partial differential equations of the Spherical Liouville, Sine- Gordon and Burgers type are constructed.
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Applications of Symmetries for Solutions of Einstein Equations solutions of differential equations in nonlinear water waves
General relativity is a physical theory which nowadays plays a key role in astrophysics and in physics and in this way it is important for a number of ambitious experiments and space missions. Einstein equations are central piece of general relativity. Einstein equations are expressed in terms of coupled system of highly nonlinear partial differential equations describing the matter content of space-time. The present work is to give an exposition of parts of the theory of partial differential equations that are needed in this subject and to represent exact solutions to Einstein equations. This book deals with various system of non linear partial differential equations corresponding to the Einstein equations for non diagonal Einstein-Rosen Metrics, Cylindrically Symmetric Null Fields, Vacuum Field Equations etc. from the view point of underlying symmetries and then to obtain their some new explicit exact solutions by using symmetry techniques like Lie symmetry analysis, symmetry reduction etc. These exact solutions play a significant for understanding of various phenomenons and are utilized for checking validity of numerical and approximation techniques and programs.
3549 RUR
Applications of Lie Group to Some Nonlinear Equations solutions of differential equations in nonlinear water waves
Keeping in view the rich treasure and wide applicability of nonlinear equations in almost every field, we have in this book carried out the application of Lie group analysis for obtaining exact solutions to nonlinear partial differential equations. In particular, this book is devoted to a wide range of applications of continuous symmetry groups to two physically important systems i.e. the (2+1)-dimensional Calogero Degasperis equation with its variable coefficients form and the (2+1)-dimensional potential Kadomstev Petviashvili equation along its generalized form. In recent years, much attention has also been paid to equations with variable coefficients as the physical situations in which nonlinear systems arise tend to be highly idealized due to assumption of constant coefficients. This has led us to undertake the study of equations with variable coefficients and to derive the admissible forms of the coefficients along with their exact solutions. The efforts are thus concentrated on finding the symmetries, reductions and exact solutions of certain nonlinear equations by using various methods.
4929 RUR
Study of point and spatial processes by methods of wave dynamics solutions of differential equations in nonlinear water waves
In present book are represented obtained by authors results of investigations of various unsteady problems of waves propagation in different media. In Introduction there are described obtained solutions of problems for three dimensional linear and nonlinear waves, including investigations of diffraction nonlinear problems, caustics, nonlinear quasi-monochromatic waves, narrow nonlinear gaussian beams, various unsteady mixed boundary value problems of elasticity, solved by Wiener-Hopf technique and derivation of solution in Smirnov-Sobolev form, exact 3D method of determination of frequencies of vibrations of magneto-elastic and piezo-electric plates and shells by derivation of transcendent equations and their numerical solution, as well as, in solution of problems of investigation of probabilities and prognosis for stochastic processes in various branches of science.
5790 RUR
Geometry of Partial Differential Equations solutions of differential equations in nonlinear water waves
The study of partial differential equations has been the object of much investigation and seen a great many advances recently. This is primarily due to the fact that certain classes of these equations fall under the category of being integrable. These kinds of equations have many useful properties such as the existence of Lax pairs, Backlund transformations, explicit solutions and the existence of a correspondence with geometric manifolds. There have also been many applications of solutions to these equations in the study of solitons and other objects which have seen applications in physics. It is the objective here to study some of these equations in a general way by using various ideas that have evolved in the evolution of the subject of differential geometry. The first sections give some introductory material related to the subject, and then the latter sections seek to apply these ideas to obtain many useful results with regard to nonlinear equations and to some examples of nonlinear equations in particular. Each chapter is self-contained and can be read on its own if desired.
5790 RUR
Impulsive Differential Equations and Applications to Some Models solutions of differential equations in nonlinear water waves
The solutions of impulsive differential equations (IDEs) are often discontinuous and are not integrable in the ordinary sense of the word as most hypotheses in differential equations normally assumed.This peculiarity makes (IDEs) not easily accessible to most existing concepts and theorems in the differential equations. Therefore the existing concepts, theories in Differential Equations need to be strengthened or new ones developed before applying to (IDEs).This book will be useful to Students and practitioners in the field and in the industry working on problems with impulsive attributes such as modeling/computer simulation of stock price and petroleum pricing, disaster management,harvesting problem, biomedical problems,engineering and so on. We utilized several interesting techniques in nonlinear analysis such as topological degree, compact operators, monotone-iterative technique, measure of non-compact maps, inequalities on cone and applied them to some practical problems including, Numerical approximation of solutions of impulsive differential equations and measure differential equations.
7790 RUR
Improved Tanh and Sech Methods for Obtaining New Exact Solutions solutions of differential equations in nonlinear water waves
Exact solutions to nonlinear evolution equations (NEEs) play an important role in nonlinear physical science, since the characteristics of these solutions may well simulate real-life physical phenomena. One of the benefits of finding new exact solutions to such nonlinear partial differential equations (PDEs) is to give a better understanding on the various characteristics of the solutions. The main task of this work is to show that our proposed methods, improved tanh and sech methods, are very efficient in solving various types of NEEs and PDEs including special equations than using classical tanh and sech methods. This efficiency is because of their rich with the multiple traveling wave solutions than classical tanh and sech methods. From the obtained results, we can not only recover the previous solutions obtained by some authors but also obtain some new and more general solitary wave, singular solitary wave and periodic solutions. Illustrating the theory of nonlinear transmission lines (NLTLs), showing the ability of NLTL to generate solitons and solving the model equation of NLTL in presence of loss are other tasks of this book.
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