Author | Marchenko, Vladimir A. author |
---|---|

Title | Nonlinear Equations and Operator Algebras [electronic resource] / by Vladimir A. Marchenko |

Imprint | Dordrecht : Springer Netherlands, 1988 |

Connect to | http://dx.doi.org/10.1007/978-94-009-2887-9 |

Descript | XVI, 158 p. online resource |

SUMMARY

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics

CONTENT

1. General Scheme -- ยง1 Generalized Derivation and Logarithmic Derivatives -- ยง2 Examples of Nonlinear Equations -- ยง3 Projection Operation -- 2. Realization of the General Scheme in Matrix Rings and N-Soliton Solutions -- ยง1 Wronsky Matrices -- ยง2 Conditions of Invertibility of Some Wronsky Matrices -- ยง3 N-Soliton Solutions of Nonlinear Equations -- ยง4 Singular Solutions of Nonlinear Equations -- 3. Realization of the General Scheme in Operator Algebras -- ยง1 Extenstion of Algebra C?(B(H0) -- ยง2 Solving Linear Equations in Algebra C?(B(H)) -- ยง3 Additional Equations -- ยง4 Choice of Parameters -- ยง5 Properties of Logarithmic Derivatives with Respect to Conjunction Operation -- ยง6 Invertibility Conditions for Operators $$ \hat{\Gamma } $$ -- 4. Classes of Solutions to Nonlinear Equations -- ยง1 Examples of Solutions to Nonlinear Equations -- ยง2 Connection with Inverse Problems of Spectral Analysis -- ยง3 KP Equation -- References

Mathematics
Partial differential equations
Mathematics
Partial Differential Equations