Solitons In Two Dimensional Shallow Water

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Solitons In Two Dimensional Shallow Water

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Author : Yuji Kodama
language : en
Publisher: SIAM
Release Date : 2018-12-10

Solitons In Two Dimensional Shallow Water written by Yuji Kodama and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-10 with Science categories.

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools?algebraic geometry, algebraic combinatorics, and representation theory, among others?are used to analyze these two-dimensional wave patterns. The author?s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.

Solitons In Two Dimensional Shallow Water

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Author : Yuji Kodama
language : en
Publisher: SIAM
Release Date : 2018-12-10

Solitons In Two Dimensional Shallow Water written by Yuji Kodama and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-10 with Science categories.

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools?algebraic geometry, algebraic combinatorics, and representation theory, among others?are used to analyze these two-dimensional wave patterns. The author?s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.?

Nonlinear Dispersive Equations

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Author : Christian Klein
language : en
Publisher: Springer Nature
Release Date : 2022-02-23

Nonlinear Dispersive Equations written by Christian Klein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-23 with Mathematics categories.

Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose–Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin–Ono, Davey–Stewartson, and Kadomtsev–Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.

Emerging Frontiers In Nonlinear Science

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Author : Panayotis G. Kevrekidis
language : en
Publisher: Springer Nature
Release Date : 2020-05-29

Emerging Frontiers In Nonlinear Science written by Panayotis G. Kevrekidis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-29 with Science categories.

This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.

Geometric Mechanics And Its Applications

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Author : Weipeng Hu
language : en
Publisher: Springer Nature
Release Date : 2023-01-01

Geometric Mechanics And Its Applications written by Weipeng Hu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Technology & Engineering categories.

To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.

Ray Methods For Nonlinear Waves In Fluids And Plasmas

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Author : Marcelo Anile
language : en
Publisher: CRC Press
Release Date : 2021-06-23

Ray Methods For Nonlinear Waves In Fluids And Plasmas written by Marcelo Anile and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Mathematics categories.

Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

Nonlinear And Modern Mathematical Physics

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Author : Solomon Manukure
language : en
Publisher: Springer Nature
Release Date : 2024-06-07

Nonlinear And Modern Mathematical Physics written by Solomon Manukure and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-07 with Mathematics categories.

This book gathers peer-reviewed, selected contributions from participants of the 6th International Workshop on Nonlinear and Modern Mathematical Physics (NMMP-2022), hosted virtually from June 17–19, 2022. Works contained in this volume cover topics like nonlinear differential equations, integrable systems, Hamiltonian systems, inverse scattering transform, Painleve's analysis, nonlinear wave phenomena and applications, numerical methods of nonlinear wave equations, quantum integrable systems, and more. In this book, researchers and graduate students in mathematics and related areas will find new methods and tools that only recently have been developed to solve nonlinear problems. The sixth edition of the NMMP workshop was organized by Florida A&M University in Tallahassee, Florida, USA, with support from the University of South Florida, Florida State University, Embry-Riddle Aeronautical University, Savannah State University, Prairie View A&M University, and Beijing Jiaotong University. The aim was to bring together researchers from around the world to present their findings and foster collaboration for future research.

Solitary Waves In Dispersive Complex Media

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Author : Vasily Y. Belashov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20

Solitary Waves In Dispersive Complex Media written by Vasily Y. Belashov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Science categories.

Deals with the theoretical, analytical and advanced numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrodinger (NLS) and derivative NLS (DNLS) classes of equations.

Physics Of Solitons

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Author : Thierry Dauxois
language : en
Publisher: Cambridge University Press
Release Date : 2006-03-09

Physics Of Solitons written by Thierry Dauxois and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-09 with Mathematics categories.

This textbook gives an instructive view of solitons and their applications for advanced students of physics.

Proceedings Of The Conference On Water Waves Theory And Experiment Howard University Usa 13 18 May 2008

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Author : M. F. Mahmood
language : en
Publisher: World Scientific
Release Date : 2010

Proceedings Of The Conference On Water Waves Theory And Experiment Howard University Usa 13 18 May 2008 written by M. F. Mahmood and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.

The objective of this book is to introduce new researchers to the rich dynamical system of water waves, and to show how (some) abstract mathematical concepts can be applied fruitfully in a practical physical problem and to make the connection between theory and experiment. It provides a coherent set of lectures on the current status of water wave theory, including identification of some open problems.