TY  - BOOK
AU  - Tarkhanov,Nikolai N.
TI  - Nonlinear Equations with Small Parameter. 
T2  - De Gruyter Series in Nonlinear Analysis and Applications ,
SN  - 9783110533835
AV  - QA427 .G54 2017
U1  - 510 23
PY  - 2018///]
CY  - Berlin, Boston : 
PB  - De Gruyter, 
KW  - Nonlinear theories
KW  - MATHEMATICS / Differential Equations / General
KW  - bisacsh
N1  - Frontmatter --; Preface --; Contents --; Introduction --; 1. The Solitary Waves Generation due to Passage through the Local Resonance --; 2. Regular Perturbation of Ill-Posed Problems --; 3. Asymptotics at Characteristic Points --; 4. Asymptotic Expansions of Singular Perturbation Theory --; 5. Asymptotic Solution of the Schrödinger Equation --; 6. The Kelvin–Helmholtz Instability --; 7. Nonlinear Cauchy Problems for Elliptic Equations --; Bibliography --; Index; restricted access; Issued also in print
N2  - This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations
UR  - https://doi.org/10.1515/9783110534979
UR  - https://www.degruyter.com/isbn/9783110534979
UR  - https://www.degruyter.com/document/cover/isbn/9783110534979/original
ER  -