| 000 | 03625nam a22005415i 4500 | ||
|---|---|---|---|
| 001 | 978-3-540-39808-0 | ||
| 003 | DE-He213 | ||
| 005 | 20190213151613.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 150519s2003 gw | s |||| 0|eng d | ||
| 020 |
_a9783540398080 _9978-3-540-39808-0 |
||
| 024 | 7 |
_a10.1007/b13714 _2doi |
|
| 050 | 4 | _aQC5.53 | |
| 072 | 7 |
_aPHU _2bicssc |
|
| 072 | 7 |
_aSCI040000 _2bisacsh |
|
| 072 | 7 |
_aPHU _2thema |
|
| 082 | 0 | 4 |
_a530.15 _223 |
| 245 | 1 | 0 |
_aDirect and Inverse Methods in Nonlinear Evolution Equations _h[electronic resource] : _bLectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2003. |
|
| 300 |
_aXI, 279 p. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
||
| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
||
| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 |
_aLecture Notes in Physics, _x0075-8450 ; _v632 |
|
| 505 | 0 | _aExact Solutions of Nonlinear Partial Differential Equations by Singularity Analysis -- The Method of Poisson Pairs in the Theory of Nonlinear PDEs -- Nonlinear Superposition Formulae of Integrable Partial Differential Equations by the Singular Manifold Method -- Hirota Bilinear Method for Nonlinear Evolution Equations -- Lie Groups, Singularities and Solutions of Nonlinear Partial Differential Equations. | |
| 520 | _aMany physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved. | ||
| 650 | 0 | _aMathematical physics. | |
| 650 | 0 | _aDifferential equations, partial. | |
| 650 | 0 | _aGlobal differential geometry. | |
| 650 | 0 | _aStatistical physics. | |
| 650 | 1 | 4 |
_aMathematical Methods in Physics. _0http://scigraph.springernature.com/things/product-market-codes/P19013 |
| 650 | 2 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
| 650 | 2 | 4 |
_aDifferential Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M21022 |
| 650 | 2 | 4 |
_aComplex Systems. _0http://scigraph.springernature.com/things/product-market-codes/P33000 |
| 650 | 2 | 4 |
_aStatistical Physics and Dynamical Systems. _0http://scigraph.springernature.com/things/product-market-codes/P19090 |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783642057533 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783540200871 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783662143926 |
| 830 | 0 |
_aLecture Notes in Physics, _x0075-8450 ; _v632 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/b13714 |
| 912 | _aZDB-2-PHA | ||
| 912 | _aZDB-2-LNP | ||
| 912 | _aZDB-2-BAE | ||
| 999 |
_c11252 _d11252 |
||