ISBN: 9783662009246

The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the in… Mehr…

The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one­ dimensional linear Schrödinger equation. Soliton theory is now a large part of theoretical and mathematical physics. An important method used to solve related equations is based on the Inverse Scattering Transform (IST). This IST method has been extended and applied to a large variety of (analytically) solvable non­ linear evolution equations, including many important examples describing phe­ nomena in nonlinear optics, solid state physics, hydrodynamics, theory of general relativity, plasma physics, etc. In the about twenty years of development the necessary mathematical tools have become rather sophisticated. They include the methods of algebraic geome­ try, the machinery of group representations, the theory of the local and nonlocal Riemann-Hilbert problem and many other "higher" levels of contemporary math­ ematics. Books > Physics Soft cover, Springer Shop<

1992, ISBN: 9783662009246

Softcover reprint of the original 1st ed. 1991, Softcover, Buch, [PU: Springer Berlin]