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| Author | : Ryogo Hirota |
| Publisher | : Cambridge University Press |
| Total Pages | : 220 |
| Release | : 2004-07-22 |
| Genre | : Mathematics |
| ISBN | : 9780521836609 |
Account of method of solving soliton equations by the inventor of the method.
| Author | : |
| Publisher | : |
| Total Pages | : 200 |
| Release | : 2004 |
| Genre | : Electronic books |
| ISBN | : 9780511214844 |
The modern version of the bilinear, or Hirota's direct, method is described here using relatively simple mathematics. As the only account in book form of the modern form of the theory, it will be essential reading for all those working in soliton theory.
| Author | : R.K. Bullough |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 403 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 3642814484 |
With contributions by numerous experts
| Author | : Angela Slavova |
| Publisher | : Springer Nature |
| Total Pages | : 483 |
| Release | : |
| Genre | : |
| ISBN | : 3031532120 |
| Author | : Harendra Singh |
| Publisher | : CRC Press |
| Total Pages | : 236 |
| Release | : 2022-02-17 |
| Genre | : Technology & Engineering |
| ISBN | : 1000540103 |
Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
| Author | : Angela Slavova |
| Publisher | : World Scientific Publishing |
| Total Pages | : 208 |
| Release | : 2018-11-16 |
| Genre | : Mathematics |
| ISBN | : 9813271620 |
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
| Author | : Robert M. Miura |
| Publisher | : Springer |
| Total Pages | : 302 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540382208 |
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
| Author | : Alwyn Scott |
| Publisher | : Routledge |
| Total Pages | : 2881 |
| Release | : 2006-05-17 |
| Genre | : Reference |
| ISBN | : 1135455570 |
In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
| Author | : Dr. K.S. Lakshmi |
| Publisher | : Allied Publishers |
| Total Pages | : 196 |
| Release | : 2017-08-10 |
| Genre | : Mathematics |
| ISBN | : 9385926780 |
Differential Equations serve as mathematical models for virtually any natural or physical phenomena in science and technology and has applications even in diverse fields such as economics, medicine, ecology, etc. The seminar was organized to throw light on the recent advances in the applications of differential equations and to provide a platform for sharing the knowledge with experts in the field with young students and researchers. The Researchers and educators in the field of differential equations were invited to attend and share their rich experience. As for everything else. so for a mathematical theory. beauty can be perceived but not explained.
| Author | : İlkay Bakırtaş |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 260 |
| Release | : 2021-01-27 |
| Genre | : Science |
| ISBN | : 1839626518 |
With this book, we aim to capture different perspectives of researchers on nonlinear optics and optical devices and we intend to cover the latest developments in optics from theoretical, numerical, and experimental aspects. The eleven selected chapters cover a variety of topics related to nonlinear optics including bright, dark, kink solitary waves in various media, magnetic solitons, lattice solitons, rogue-waves, solid-state lasers, laser cladding, optical sensors, optical vortices, and molecular switches. The book is intended to draw the attention of scientists in academia, as well as researchers and engineers in industry, since the field has a significant potential for the production and design of novel optical devices and other technological applications.
