The main attention in the book is given to the methods of constructing analytical solutions of nonlinear differential equations. For the equations integrated by the reverse problem of scattering: the equations of the Corteveg-de Vriz, the non-linear equation of Schrödinger and the Sinus-Gordon equation-the pairs of laxa and the transformation of backlund are presented, as well as the schemes for solving the problems of the cat. For a number of other non -linear differential equations, methods for finding exact solutions are proposed.
To demonstrate the methods presented in the book, the most popular nonlinear differential equations were selected: the Kortevega-de-Vriza equation, the non-linear equation of the Schrödinger, the Sinus-Gordon equation, the Kuramot-Sivashinsky equation, the Ginzburg-Landau equation, the equation of Kolmogorov-Petrovsky-scripture, the equity Burgers-Haxli, an equation of nonlinear thermal conductivity and well-known systems of differential equations: the Lorentz system and the Henon-Heleka system.
The book can be considered as a reference on the very head …
Author
Kudryashov Nikolay Alekseevich
Publisher
ID Intellect, 2010
Genre
Physical sciences. Astronomy
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