New Trends in Integrability and Partial Solvability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Trends in Integrability and Partial Solvability write by A.B. Shabat. This book was released on 2012-12-06. New Trends in Integrability and Partial Solvability available in PDF, EPUB and Kindle. Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002
Recent Trends in Formal and Analytic Solutions of Diff. Equations
Recent Trends in Formal and Analytic Solutions of Diff. Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Trends in Formal and Analytic Solutions of Diff. Equations write by Galina Filipuk. This book was released on 2023-02-09. Recent Trends in Formal and Analytic Solutions of Diff. Equations available in PDF, EPUB and Kindle. This volume contains the proceedings of the conference on Formal and Analytic Solutions of Diff. Equations, held from June 28–July 2, 2021, and hosted by University of Alcalá, Alcalá de Henares, Spain. The manuscripts cover recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, moment differential equations, etc. Also discussed are related topics such as summability of formal solutions and the asymptotic study of their solutions. The volume is intended not only for researchers in this field of knowledge but also for students who aim to acquire new techniques and learn recent results.
Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations
Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations write by Pham Loi Vu. This book was released on 2023-05-15. Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations available in PDF, EPUB and Kindle. Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Bӓckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.
Discrete Systems and Integrability
Discrete Systems and Integrability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Systems and Integrability write by J. Hietarinta. This book was released on 2016-09. Discrete Systems and Integrability available in PDF, EPUB and Kindle. A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
Isochronous Systems
Isochronous Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Isochronous Systems write by Francesco Calogero. This book was released on 2008-02-07. Isochronous Systems available in PDF, EPUB and Kindle. A dynamical system is called isochronous if it features in its phase space an open, fully-dimensional region where all its solutions are periodic in all its degrees of freedom with the same, fixed period. Recently a simple transformation has been introduced, applicable to quite a large class of dynamical systems, that yields autonomous systems which are isochronous. This justifies the notion that isochronous systems are not rare.In this book the procedure to manufacture isochronous systems is reviewed, and many examples of such systems are provided. Examples include many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs).The book shall be of interest to students and researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It might be used as a basic textbook, or as backup material for an undergraduate or graduate course.
