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Saturday, August 1, 2020 | History

2 edition of Multi-soliton interactions and the inverse problem of wave crests found in the catalog.

Multi-soliton interactions and the inverse problem of wave crests

Pearu Peterson

Multi-soliton interactions and the inverse problem of wave crests

by Pearu Peterson

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  • 6 Currently reading

Published by TTU Press in Tallinn .
Written in English


Edition Notes

StatementPearu Peterson.
SeriesThesis on natural and exact sciences. B -- 10
Classifications
LC ClassificationsMLCM 2008/43318 (Q)
The Physical Object
Pagination108 p. :
Number of Pages108
ID Numbers
Open LibraryOL22992575M
ISBN 109985592336
LC Control Number2006530908

Abstract. A detailed description of multi-soliton (more than two) interactions is needed for many practical applications for solving both the direct and inverse problems in multi-directional wave phenomenon (for example, surface waves). In this paper a strict novel formalism for constructing multi-soliton solutions of. Engelbrecht, J. (ed.). Estonian Academy of Sciences year book Tallinn, , [1] p. P. Multi-soliton interactions and the inverse problem of wave crests. Salupere, A. Nonlinear waves in solids and inverse problems // Abstract Book, IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains: August 20–

Nonlinear components of wakes from large high-speed ships at times carry a substantial part of the wake energy and behave completely differently compared to the classical Kelvin wave system. This overview makes an attempt to summarize the descriptions of nonlinear parts of a . Peterson P, van Groesen E () A direct and inverse problem for wave crests modelled by interactions of two solitons. Physica D – MathSciNet ADS Google Scholar

This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects of soliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations. Pearu Peterson, Doctor's Degree, , (sup) Jüri Engelbrecht; Embrecht van Groesen, Mitmiksolitonide vastastikmõjud ja laineharjade pöördülesanne (Multi-soliton interactions and the inverse problem of wave crests), Tallinn University of Technology.


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Multi-soliton interactions and the inverse problem of wave crests by Pearu Peterson Download PDF EPUB FB2

All new concepts are illustrated for two-soliton interactions, examples are given also for three- and five-soliton interactions. For exemplifying models of soliton interactions, the KdV, KdV-Sawada-Kotera, and KP equations are used.

As a practical application of these findings, an inverse problem of wave crests is introduced. The uniqueness of a solution to the inverse problem is proved for the KP two-soliton. P. Peterson, Multi-soliton interactions and the inverse problem of wave crests, Ph.D.

Thesis, Tallinn, Chapter III, Cited by: 4. A detailed description of multi-soliton (more than two) interactions is needed for many practical applications for solving both the direct and inverse problems in multi-directional wave.

In a previous paper [Physica DNo. 3–4, – (; Zbl )], the authors introduced the inverse problem for wave crests and gave a solution strategy for two-wave interactions.

In general, solving the inverse problem of wave patterns modeled by multi-soliton solution, consists of the following four main steps: 1. Measure the shifts of the wave crests and state the equations relating these measurements with the parameters in the wave vectors Cited by: Peterson P, van Groesen E () A direct and inverse problem for wave crests modelled by interactions of two solitons.

Physica D – MathSciNet zbMATH Google Scholar Multi-soliton interactions and the inverse problem of. wave crests, Oblique solitary-wave interaction is well-studied in various fields of physics; however, this process in the ocean has. Multi-soliton interactions and the inverse problem of wave crests.

PhD Thesis, Tallinn Technical University, November [Peterson, MSc, ] Pearu Peterson. Travelling waves in nonconservative media with dispersion. MSc Thesis. Tallinn Technical University, June The book is organized in four parts: (1) an overview of coastal engineering, using case studies to illustrate problems; (2) hydrodynamics of the coastal.

Figure 1: The setup to observe soliton interactions. To achieve the necessary accuracy we use the iterative implementation of the split-step Fourier method (Figure 2).

Figure 2: Iterative implementation of the split-step Fourier method. At first we consider interaction between two identical in-phase solitons. In this case they form a bound pair.

Abstract. To predict the wave parameters from the inter-action patterns of waves (the inverse problem), the corresponding direct problem needs to be solved.

In this paper interaction patterns of multi-soliton so-lutions of KdV type equations are constructed. The connection between the multi-soliton interaction pat.

In a previous paper [Physica D (3–4) () ], the inverse problem for wave crests was introduced and a solution strategy for two-wave interactions was given. Here these solutions are actually constructed, in particular for the cases with small interaction angle, moderate phase shifts, and/or symmetric interactions.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. To predict the wave parameters from the inter-action patterns of waves (the inverse problem), the corresponding direct problem needs to be solved.

In this paper interaction patterns of multi-soliton so-lutions of KdV type equations are constructed. The connection between the multi-soliton interaction. Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma. M S Alam 1,3, for the significance of the problems related to the astrophysical and laboratory plasmas, we study the interaction processes of the IA single- and multi-solitons, and their phase shifts as well as rogue waves in an.

() A direct and inverse problem for wave crests modelled by interactions of two solitons. Physica D: Nonlinear Phenomena() A Coupled Korteweg-de Vries System and Mass Exchanges Among Solitons.

Explicit expressions are found for a multi-soliton solution of the system of equations describing the interaction of waves on thex,y plane. The proof of all necessary statements follows from the theory of matrices and is not based on the inverse scattering method.

The obtained results are closely related to some problems of mathematical physics. Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solu- tion of the Kadomtsev-Petviashvili equation. The wave sys- tem is decomposed into the incoming waves and the interac- tion soliton that represents the particularly high wave hump in the crossing area of the waves.

Shown is that extreme surface elevations up to four times. Männikus R., Torsvik T., Soomere T. Sõru sadama kai nr 1 pikendamise mõju setete transpordile. - Tallinn: Tallinna Tehnikaülikooli Küberneetika Instituut, [Laboratory of] Wave. The relation between the soliton polarizations and the corresponding properties of the linear scattering data of the inverse scattering problem, associated with the integrable Eqs.

(1), is explained in Ref. [6] for the two-component case (M =2), and these results can be generalized to an arbitrary number of components [7].

A direct and inverse problem for wave crests modelled by interactions of two solitons (kaasautor E. van Groesen). // Physica D, () Sensitivity of the inverse wave crest problem (kaasautor E. van Groesen). // Wave Motion, 34 () Reconstruction of multi-soliton interactions using crest data for (2+1)-dimensional KdV type equations.

Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Tranform.

Their aim is to present the essence of inverse scattering clearly, rather than 5/5(1).The inverse problems are formulated and solved with the aid of the matrix Riemann-Hilbert problems, and the reconstruction formulas, trace formulas, and theta conditions are also posed.

In particular, we present the general solutions for the focusing mKdV equation with NZBCs and both simple and double poles, and for the defocusing mKdV equation.Engelbrecht, J.

(ed.). Estonian Academy of Sciences year book Tallinn,[1] p. P. Multi-soliton interactions and the inverse problem of wave crests.

A., Salupere, A. Nonlinear waves in solids and inverse problems // Abstract Book, IUTAM Symposium on Computational Mechanics of Solid Materials at.