Slowly Varying Oscillations And Waves: From Basics To Modernity

The beauty of theoretical science is that it describes physical, biological, etc. phenomena as similar mathematical objects through differential equations. In the 20th century, the theory of oscillations and waves emerged as unifying concepts, applying similar methods and equations to diverse physical problems. This book discusses oscillations and waves with slowly varying parameters, including nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. Examples range from van der Pol oscillators and pendulums to oceanography, nonlinear optics, acoustics, and biophysics. The last chapter presents formal asymptotic perturbation schemes for these classes.

Format: Hardback
Length: 372 pages
Publication date: 15 April 2022
Publisher: World Scientific Publishing Co Pte Ltd

The theoretical science holds a captivating allure, as it reveals the remarkable ability to describe diverse physical, biological, and other phenomena through the lens of similar mathematical objects. By employing differential equations or other mathematical frameworks, these phenomena can be likened to one another, offering a unified understanding.

In the 20th century, a significant milestone was reached with the emergence of the theories of oscillations and waves, which unified these diverse fields by applying similar methods and equations to seemingly unrelated physical problems. This breakthrough paved the way for a deeper exploration of the underlying principles governing these phenomena.

Oscillatory processes, characterized by slow variations in parameters like amplitude and frequency, are prevalent in a wide range of applications. This slow dynamics is a defining feature of oscillatory systems, and it is observed in various natural and artificial systems. From the swinging of a pendulum to the operation of lasers, oscillators serve as physical examples of this behavior.

Similarly, wave processes exhibit similar characteristics. Waves propagate through space, carrying energy and information from one point to another. They can be observed in ocean waves, sound waves, light waves, and even in the behavior of particles in matter. Wave phenomena are characterized by their ability to interact with boundaries, reflect, and diffract, leading to a rich tapestry of phenomena.

This book delves into the realm of oscillations and waves, focusing on problems associated with slowly varying parameters. It explores a wide range of topics, including nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. Each chapter provides detailed explanations and examples, drawing from various fields such as oceanography, nonlinear optics, acoustics, and biophysics.

In addition to the theoretical aspects, the book also presents more formal asymptotic perturbation schemes for the classes of oscillators and waves considered throughout the preceding chapters. These schemes offer valuable tools for analyzing and predicting the behavior of complex systems, providing insights into their underlying dynamics and behavior.

In conclusion, the beauty of theoretical science lies in its ability to bridge the gap between seemingly disparate fields, revealing the underlying similarities and connections that govern the natural world. The theories of oscillations and waves serve as prime examples of this phenomenon, offering a unified framework for understanding diverse physical phenomena and paving the way for further advancements in scientific research and technology.

ISBN-13: 9789811247484