Classical and Quantum Nonlinear Integrable Systems: Theory by A. Kundu

By A. Kundu

Masking either classical and quantum types, nonlinear integrable structures are of substantial theoretical and sensible curiosity, with functions over quite a lot of subject matters, together with water waves, pin versions, nonlinear optics, correlated electron structures, plasma physics, and reaction-diffusion approaches. Comprising one half on classical theories and purposes and one other on quantum facets, Classical and Quantum Nonlinear Integrable platforms: concept and alertness studies the advances made in nonlinear integrable platforms, with emphasis at the underlying recommendations instead of technical information. It types an excellent introductory textbook in addition to an invaluable reference for experts.

Show description

Read or Download Classical and Quantum Nonlinear Integrable Systems: Theory and Application (Series in Mathematical and Computational Physics) PDF

Best physics books

Halogen oxides- radicals, sources and reservoirs in the laboratory and in the atmosphere

Learn task in atmospheric chemistry has persevered to speed up lately, and there's now heightened public expertise of the environmental concerns within which it performs a component. This publication appears on the new insights and interpretations afforded by way of the hot advances, and locations in context those advancements.

Econophysics of Markets and Business Networks

Econophysicists have lately been particularly profitable in modelling and analysing numerous monetary platforms like buying and selling, banking, inventory and different markets. The statistical behaviour of the underlying networks in those structures have additionally been pointed out and characterized lately. This e-book studies the present econophysics researches within the constitution and functioning of those advanced monetary community structures.

Additional info for Classical and Quantum Nonlinear Integrable Systems: Theory and Application (Series in Mathematical and Computational Physics)

Sample text

83), we have K(x, y, t) = −C02 e8κ 3 t −κ(x+y) [1 + (C02 /2κ) e8κ 3 t −2κx ] . 77) as d K(x, x + 0, t) dx = −2∂K(x, y, t)/∂x|y=x − 2∂K(x, y, t)/∂y|y=x u(x, t) = −2 = −2κ 2 e−2κ(x−4κ 2 t )−2δ [1 + e−2κ(x−4κ t )−2δ ]2 2 = −2κ sech2 [κ(x − 4κ 2t) + δ]. 32) obtained by the Hirota method. 2 Two-soliton solution Again, let us consider a reflectionless potential such that R(k, t) = 0 but now with two bound states (example: u(x) = −6 sech2 x has two bound states with λ1 = −4, λ2 = −1), specified by the discrete values κ1 and κ2 and the corresponding Copyright © 2003 IOP Publishing Ltd.

Examples of these various situations √ are, respectively: the PDE ux ut + uuxt = 0 with the general solution u = f (x) + g(t), which presents movable critical singularities and can be transformed into the d’Alembert equation; the Burgers PDE ut + uxx + 2uux = 0, linearizable into the heat equation ψt + ψxx = 0; the KdV PDE ut + uxxx − 6uux = 0, which is integrable by the inverse spectral transform (IST) [19]; and the Liouville PDE uxt + eu = 0, which possesses a BT to the d’Alembert equation ψxt = 0.

Solving them, one obtains h1 (x, t) and h2 (x, t). 89a) where γi = κi x − 4κi3t − δi δi = 1 log 2 2 Ci0 (κ2 − κ1 ) 2κi (κ2 + κ1 ) i = 1, 2. 6, with appropriate scale change and redefinition of parameters. 76b) as N F (x + y, t) = Cn2 (t) e−κn (x+y) = n=1 = N Cn e−κn x Cn e−κn y n=1 gn (x, t)gn (y, t) gn (x, t) = Cn (t) e−κn x . 90) Then defining N K(x, y) = ωn (x)gn (y) n=1 Copyright © 2003 IOP Publishing Ltd. 76), we obtain ∞ N ωm (x) + gm (x) + ωn (x) gm (z)gn (z) dz = 0. 93a) x ω(x) = (ω1 (x), ω2 (x), .

Download PDF sample

Rated 4.22 of 5 – based on 25 votes