Discrete and continuous nonlinear Schrödinger systems /
Ablowitz, Mark J.,
Discrete and continuous nonlinear Schrödinger systems / Discrete & Continuous Nonlinear Schrödinger Systems M.J. Ablowitz, B. Prinari, A.D. Trubatch. - Cambridge : Cambridge University Press, 2004. - 1 online resource (ix, 257 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 302 . - London Mathematical Society lecture note series ; 302. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Introduction -- Nonlinear Schrd̲inger equation (NLS) -- Integrable discrete nonlinear Schrd̲inger equation (IDNLS) -- Matrix nonlinear Schrd̲inger equation (MNLS) -- Integrable discrete matrix NLS equation (IDMNLS). 1. 2. 3. 4. 5
In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.
9780511546709 (ebook)
Schrödinger equation.
Nonlinear theories.
Inverse scattering transform.
QC174.26.W28 / A26 2004
530.12/4
Discrete and continuous nonlinear Schrödinger systems / Discrete & Continuous Nonlinear Schrödinger Systems M.J. Ablowitz, B. Prinari, A.D. Trubatch. - Cambridge : Cambridge University Press, 2004. - 1 online resource (ix, 257 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 302 . - London Mathematical Society lecture note series ; 302. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Introduction -- Nonlinear Schrd̲inger equation (NLS) -- Integrable discrete nonlinear Schrd̲inger equation (IDNLS) -- Matrix nonlinear Schrd̲inger equation (MNLS) -- Integrable discrete matrix NLS equation (IDMNLS). 1. 2. 3. 4. 5
In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.
9780511546709 (ebook)
Schrödinger equation.
Nonlinear theories.
Inverse scattering transform.
QC174.26.W28 / A26 2004
530.12/4