By C. Rogers, W. K. Schief

ISBN-10: 0511020546

ISBN-13: 9780511020544

ISBN-10: 0521012880

ISBN-13: 9780521012881

ISBN-10: 052181331X

ISBN-13: 9780521813310

This publication describes the striking connections that exist among the classical differential geometry of surfaces and glossy soliton concept. The authors additionally discover the huge physique of literature from the 19th and early 20th centuries via such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on differences of privileged sessions of surfaces which depart key geometric houses unchanged. popular among those are Bäcklund-Darboux ameliorations with their notable linked nonlinear superposition rules and significance in soliton idea.

**Read or Download Backlund & Darboux Transformations PDF**

**Similar waves & wave mechanics books**

**Seth D. Bergmann's Compiler design: theory, tools, and examples PDF**

This is often an introductory point textual content for compiler layout classes, that emphasizes challenge fixing talents. The strategies are basically awarded with sampler difficulties and diagrams to demonstrate the innovations. The textual content additionally covers lex and yacc compiler producing instruments in UNIX.

**Download e-book for iPad: Solitons, instantons, and twistors by Maciej Dunajski**

So much nonlinear differential equations coming up in common sciences admit chaotic habit and can't be solved analytically. Integrable structures lie at the different severe. They own typical, reliable, and good behaved recommendations referred to as solitons and instantons. those ideas play vital roles in natural and utilized arithmetic in addition to in theoretical physics the place they describe configurations topologically diverse from vacuum.

**Read e-book online Quantum Invariants: A Study of Knot, 3-Manifolds, and Their PDF**

An in depth and self-contained presentation of quantum and similar invariants of knots and 3-manifolds. Polynomial invariants of knots, corresponding to the Jones and Alexander polynomials, are developed as quantum invariants, in different phrases, invariants derived from representations of quantum teams and from the monodromy of strategies to the Knizhnik-Zamolodchikov equation.

**Read e-book online Wave phenomena PDF**

"The fabric is fantastically selected and brilliantly written … the language is apparent, direct and rigorous … a great addition to the library of any physicist. " — Physics at the present time. This lucidly written textual content emphasizes optics and acoustics, with significant emphasis put on constructing a detailed connection among mathematical expressions and the linked actual principles.

- Beyond Einstein: the cosmic quest for the theory of the universe
- Methods of bosonic and fermionic path integrals representations: continuum random geometry in quantum field theory
- Renormalization: An Introduction (Theoretical and Mathematical Physics)
- Spheroidal wave functions in electromagnetic theory
- The wave equation on a curved space-time
- Moonshine, the Monster, and Related Topics: Joint Research Conference on Moonshine, the Monster, and Related Topics June 18-23, 1994 Mount Holyoke ... Massachusetts

**Extra info for Backlund & Darboux Transformations**

**Example text**

25) and leaves it invariant. 25) holds: otherwise the compatibility condition uv = vu is not satisﬁed. • B contains a parameter  = tan( /2) injected into the underlying Bianchi transformation by a Lie group invariance. 26) associated with pseudospherical surfaces parametrised by arc length along asymptotic lines. 26) induces the B¨acklund transformation B operating at the nonlinear level. In that B represents a correspondence between solutions of the same equation, it is commonly termed an auto-B¨acklund transformation.

70), the two-soliton solution 2 + 1 1 − 2 sin sinh 2 2 . 6. A two-soliton pseudospherical surface. 89). 6. 4 Breathers There exists an important subclass of entrapped periodic two-soliton solutions known as breathers. Here, an analytic expression for the breather solution is obtained via the permutability theorem, and associated pseudospherical surfaces are constructed. 91), where i = 1 2i 1 + i2 x − 1 − i2 y . 4 Pseudospherical Soliton Surfaces. 96) with = [1 − (c2 + d 2 )]x − [1 + (c2 + d 2 )]y and = [1 + (c2 + d 2 )]x − [1 − (c2 + d 2 )]y.

If we write d = p/q, where p and q are co-prime integers with p < q, then the period of the breather solution is 2q/ p. 7. 7. Stationary breather pseudospherical surfaces [181]: p q = 14 , 34 , 15 , 12 . 5 Parallel Surfaces. 89), one can obtain the position vector of the pseudospherical surfaces associated with N-soliton solutions of the sineGordon equation as generated via iteration of the permutability theorem. Exercises 1. 89). 2. 93) over a range which depicts both the nonlinear interaction and eventual decomposition into two separate single soliton solutions.

### Backlund & Darboux Transformations by C. Rogers, W. K. Schief

by Anthony

4.5