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1 Luo, Albert C. J Two-Dimensional Quadratic Nonlinear Systems I11975 2021 eBook  
2 Boos, Jens Effects of Non-locality in Gravity and Quantum Theory I11881 2021 eBook  
3 Zhu, Yichao Equations and Analytical Tools in Mathematical Physics I11851 2021 eBook  
4 ??chsner, Andreas Classical Beam Theories of Structural Mechanics I11828 2021 eBook  
5 Yoshida, Kentaroh Yang???Baxter Deformation of 2D Non-Linear Sigma Models I11819 2021 eBook  
6 Marinca, Vasile Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems I11650 2021 eBook  
7 Grigorieva, Elena V Asymptotic Representation of Relaxation Oscillations in Lasers I10175 2017 eBook  
8 Schuch, Dieter Quantum Theory from a Nonlinear Perspective I10013 2018 eBook  
9 Maximon, Leonard C Differential and Difference Equations I09655 2016 eBook  
10 Papachristou, Costas J Aspects of Integrability of Differential Systems and Fields I09485 2019 eBook  
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TitleTwo-Dimensional Quadratic Nonlinear Systems : Volume II: Bivariate Vector Fields
Author(s)Luo, Albert C. J
PublicationSingapore, Springer Nature Singapore, 2021.
DescriptionX, 445 p. 117 illus., 113 illus. in color : online resource
Abstract NoteThe book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering
ISBN,Price9789811678691
Keyword(s)1. Applied Dynamical Systems 2. COMPLEX SYSTEMS 3. DIFFERENTIAL EQUATIONS 4. DYNAMICAL SYSTEMS 5. DYNAMICS 6. EBOOK 7. EBOOK - SPRINGER 8. NONLINEAR THEORIES 9. SYSTEM THEORY
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TitleEffects of Non-locality in Gravity and Quantum Theory
Author(s)Boos, Jens
PublicationCham, Springer International Publishing, 2021.
DescriptionXIX, 210 p. 37 illus., 33 illus. in color : online resource
Abstract NoteThis thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. ???Non-locality??? is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantum mechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a ???non-local intuition??? which may serve as a stepping stone for studies of the full, non-linear problem of non-locality
ISBN,Price9783030829100
Keyword(s)1. Classical and Quantum Gravity 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. Fundamental concepts and interpretations of QM 6. GRAVITATION 7. MATHEMATICAL PHYSICS 8. QUANTUM PHYSICS
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TitleEquations and Analytical Tools in Mathematical Physics : A Concise Introduction
Author(s)Zhu, Yichao
PublicationSingapore, Springer Nature Singapore, 2021.
DescriptionXII, 252 p. 37 illus., 29 illus. in color : online resource
Abstract NoteThis book highlights a concise and readable introduction to typical treatments of partial differential equations in mathematical physics. Mathematical physics is regarded by many as a profound discipline. In conventional textbooks of mathematical physics, the known and the new pieces of knowledge often intertwine with each other. The book aims to ease readers' struggle by facilitating a smooth transition to new knowledge. To achieve so, the author designs knowledge maps before each chapter and provides comparative summaries in each chapter whenever appropriate. Through these unique ways, readers can clarify the underlying structures among different equations and extend one's vision to the big picture. The book also emphasizes applications of the knowledge by providing practical examples. The book is intended for all those interested in mathematical physics, enabling them to develop a solid command in using partial differential equations to solve physics and engineering problems in a not-so-painful learning experience
ISBN,Price9789811654411
Keyword(s)1. Applications of Mathematics 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. Mathematical Methods in Physics 6. MATHEMATICAL PHYSICS 7. MATHEMATICS
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TitleClassical Beam Theories of Structural Mechanics
Author(s)??chsner, Andreas
PublicationCham, Springer International Publishing, 2021.
DescriptionXIII, 186 p. 160 illus., 70 illus. in color : online resource
Abstract NoteThis book provides a systematic and thorough overview of the classical bending members based on the theory for thin beams (shear-rigid) according to Euler-Bernoulli, and the theories for thick beams (shear-flexible) according to Timoshenko and Levinson. The understanding of basic, i.e., one-dimensional structural members, is essential in applied mechanics. A systematic and thorough introduction to the theoretical concepts for one-dimensional members keeps the requirements on engineering mathematics quite low, and allows for a simpler transfer to higher-order structural members. The new approach in this textbook is that it treats single-plane bending in the x-y plane as well in the x-z plane equivalently and applies them to the case of unsymmetrical bending. The fundamental understanding of these one-dimensional members allows a simpler understanding of thin and thick plate bending members. Partial differential equations lay the foundation to mathematically describe the mechanical behavior of all classical structural members known in engineering mechanics. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, these partial differential equations that describe the physical problem can be derived. Nevertheless, the fundamental knowledge from the first years of engineering education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills, might be required to master this topic
ISBN,Price9783030760359
Keyword(s)1. CONTINUUM MECHANICS 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. Mechanics, Applied 6. Solid Mechanics 7. SOLIDS
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TitleYang???Baxter Deformation of 2D Non-Linear Sigma Models : Towards Applications to AdS/CFT
Author(s)Yoshida, Kentaroh
PublicationSingapore, Springer Nature Singapore, 2021.
DescriptionXII, 70 p. 2 illus : online resource
Abstract NoteIn mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold???Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang???Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang???Baxter deformation to string theory are also described briefly.
ISBN,Price9789811617034
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. MATHEMATICAL PHYSICS 5. SPECIAL FUNCTIONS
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TitleOptimal Auxiliary Functions Method for Nonlinear Dynamical Systems
Author(s)Marinca, Vasile;Herisanu, Nicolae;Marinca, Bogdan
PublicationCham, Springer International Publishing, 2021.
DescriptionXIII, 479 p. 442 illus., 414 illus. in color : online resource
Abstract NoteThis book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of ???optimal auxiliary functions??? which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books ???Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches???, Springer-2011 and ???The Optimal Homotopy Asymptotic Method. Engineering Applications???, Springer-2015
ISBN,Price9783030756536
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. Engineering Fluid Dynamics 5. FLUID MECHANICS 6. FLUIDS 7. Soft condensed matter 8. Surfaces (Technology) 9. Surfaces, Interfaces and Thin Film 10. THERMODYNAMICS 11. THIN FILMS
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TitleAsymptotic Representation of Relaxation Oscillations in Lasers
Author(s)Grigorieva, Elena V;Kaschenko, Sergey A
PublicationCham, Springer International Publishing, 2017.
DescriptionVIII, 230 p. 73 illus : online resource
Abstract NoteIn this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations
ISBN,Price9783319428604
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. Engineering Fluid Dynamics 5. FLUID MECHANICS 6. LASERS 7. MATHEMATICAL PHYSICS 8. Optics, Lasers, Photonics, Optical Devices 9. ORDINARY DIFFERENTIAL EQUATIONS 10. PHOTONICS 11. Theoretical, Mathematical and Computational Physics
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TitleQuantum Theory from a Nonlinear Perspective : Riccati Equations in Fundamental Physics
Author(s)Schuch, Dieter
PublicationCham, Springer International Publishing, 2018.
DescriptionXIV, 258 p. 15 illus., 7 illus. in color : online resource
Abstract NoteThis book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws
ISBN,Price9783319655949
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. History and Philosophical Foundations of Physics 6. ORDINARY DIFFERENTIAL EQUATIONS 7. PHYSICS 8. QUANTUM PHYSICS 9. STATISTICAL PHYSICS
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TitleDifferential and Difference Equations : A Comparison of Methods of Solution
Author(s)Maximon, Leonard C
PublicationCham, Springer International Publishing, 2016.
DescriptionXV, 162 p : online resource
Abstract NoteThis book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green???s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer???s rule, a detailed consideration of the role of the superposition principal in the Green???s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients
ISBN,Price9783319297361
Keyword(s)1. APPLIED MATHEMATICS 2. Difference and Functional Equations 3. DIFFERENCE EQUATIONS 4. DIFFERENTIAL EQUATIONS 5. EBOOK 6. EBOOK - SPRINGER 7. ENGINEERING MATHEMATICS 8. FUNCTIONAL EQUATIONS 9. Mathematical and Computational Engineering 10. Mathematical Applications in the Physical Sciences 11. Mathematical Methods in Physics 12. MATHEMATICAL PHYSICS 13. ORDINARY DIFFERENTIAL EQUATIONS 14. PHYSICS
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TitleAspects of Integrability of Differential Systems and Fields : A Mathematical Primer for Physicists
Author(s)Papachristou, Costas J
PublicationCham, Springer International Publishing, 2019.
DescriptionVIII, 94 p. 20 illus : online resource
Abstract NoteThis book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and B??cklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency
ISBN,Price9783030350024
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. Mathematical Methods in Physics 5. MATHEMATICAL PHYSICS 6. ORDINARY DIFFERENTIAL EQUATIONS 7. PARTIAL DIFFERENTIAL EQUATIONS 8. PHYSICS
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