# eBook Darboux Transformations and Solitons (Springer Series in Nonlinear Dynamics) download

## by V B Matveev

**ISBN:**3540506608

**Author:**V B Matveev

**Publisher:**Springer (January 1, 1991)

**Language:**English

**Pages:**120

**ePub:**1493 kb

**Fb2:**1183 kb

**Rating:**4.8

**Other formats:**txt lit lrf mbr

**Category:**Math Sciences

**Subcategory:**Physics

Series: Springer Series in Nonlinear Dynamics.

Series: Springer Series in Nonlinear Dynamics. Paperback: 120 pages. Publisher: Springer (January 1, 1991). ISBN-13: 978-3540506607. Shipping Weight: 1. ounces. Back to top. Get to Know Us. Careers.

Springer Series in Nonlinear Dynamics. Darboux Transformations and Solitons. The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one dimensional linear Schrödinger equation. Soliton theory is now a large part of theoretical and mathematical physics. Springer Series in Nonlinear Dynamics.

Salle, Darboux transformations and solitons (Springer Series in Nonlinear Dynamics, Springer-Verlag, Berlin, 1991). The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on some non-abelian Lie group, is studied and the solutions are shown to be expressed in terms of quasideterminants. As an explicit example, the Darboux transformation on scalar solutions to the system based on the Lie group SU(2) is discussed in detail and the solutions are shown to be expressed as ratios of determinants.

New & Forthcoming Titles Springer Series in Nonlinear Dynamics. Titles in this series. New & Forthcoming Titles. Home New & Forthcoming Titles.

PDF Darboux transformation is one of the methods used in solving nonlinear evolution equation. V. B. Matveev and M. A. Salle, Darboux Transforma-. tions and Solitons, Springer Series in Nonlinear Dynamics. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the nonlinear evolution equation .

Darboux Transformations And Solitons book. Darboux Transformations and Solitons (Springer Series in Nonlinear Dynamics). 3540506608 (ISBN13: 9783540506607).

In this book, the authors develop Darboux's idea to solve linear and nonlinear partial differential .

In this book, the authors develop Darboux's idea to solve linear and nonlinear partial differential equations arising in soliton theory: the non-stationary linear Schrodinger equation, Korteweg-de Vries and li equations, the Davey Stewartson system, Sine-Gordon and nonlinear Schrodinger equations 1+1 and 2+1 Toda lattice equations, and many others. By using the Darboux transformation, the authors construct and examine the asymptotic behaviour of multisoliton solutions interacting with an arbitrary background

oceedings{, title {Darboux Transformations and Solitons}, author {Vladimir Borisovich .

oceedings{, title {Darboux Transformations and Solitons}, author {Vladimir Borisovich Matveev and Mikhail A. Salle}, year {1992} }. Vladimir Borisovich Matveev, Mikhail A. Salle. In this book, the authors develop Darboux's idea to solve linear and nonlinear partial differential equations arising in soliton theory: the non-stationary linear Schrodinger equation, Korteweg-de Vries and li equations, the Davey Stewartson system, Sine-Gordon and nonlinear Schrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.

Items related to Darboux Transformations and Solitons (Springer Series. By using the Darboux transformation, the authors construct and examine the asymptotic behaviour of multisoliton solutions interacting with an arbitrary background. V B Matveev Darboux Transformations and Solitons (Springer Series in Nonlinear Dynamics). ISBN 13: 9783540506607. In particular, the approach is useful in systems where an analysis based on the inverse scattering transform is more difficult.

Darboux transformations and solitons, Springer Series in Nonlinear Dynamics, Springer-Verlag (1991). and Leble S. Inverse Problems 11, 925-937, (1995). Figure 1: line soliton. Figure 2: Interaction of two line solitons. Figure 3: One dromion. Figure 4b: Interaction of two dromions, t 0. Figure 5: 2+1 dromion.