Integrable nonautonomous KdV systems

Download

119428.pdf

Date

2002

Author

Turhan, Refik

Metadata

Show full item record

Item Usage Stats

108
views

0
downloads

Multi-component Korteweg-de Vries (KdV) type of nonautonomous systems in (1+1) dimensions are classified for integrability via existence of a recursion op erator having a certain general form. Integrability conditions are obtained for sys tems with arbitrary number of components. From these conditions two-component integrable systems are explicitly obtained. All the found integrable two-component nonautonomous systems are investigated for their transformability to autonomous systems.

Subject Keywords

Korteweg-de Vries equation, Nonlinear, Recursive functions, Symmetry (Physics), Evolution equations, Differential equations, Evolution systems, Integrability, Symmetry, Recursion, Operator

URI

https://hdl.handle.net/11511/12802

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

The finite element method over a simple stabilizing grid applied to fluid flow problems Aydın, Selçuk Han; Tezer-Sezgin, Münevver; Department of Scientific Computing (2008) We consider the stabilized finite element method for solving the incompressible Navier-Stokes equations and the magnetohydrodynamic (MHD) equations in two dimensions. The well-known instabilities arising from the application of standard Galerkin finite element method are eliminated by using the stabilizing subgrid method (SSM), the streamline upwind Petrov-Galerkin (SUPG) method, and the two-level finite element method (TLFEM). The domain is discretized into a set of regular triangular elements. In SSM, the...
Normalizers in homogeneous symmetric groups Güven, Ülviye Büşra; Kuzucuoğlu, Mahmut; Department of Mathematics (2017) We study some properties of locally finite simple groups, which are the direct limit of finite (finitary) symmetric groups of (strictly) diagonal type. The direct limit of the finite (finitary) symmetric groups of strictly diagonal type is called textbf{homogeneous (finitary) symmetric groups}. In cite{gkk}, Kegel, Kuzucuou{g}lu and myself studied the structure of centralizer of finite groups in the homogeneous finitary symmetric groups. Instead of strictly diagonal embeddings, if we have diagonal embedding...
On finite groups admitting a fixed point free abelian operator group whose order is a product of three primes Mut Sağdıçoğlu, Öznur; Ercan, Gülin; Department of Mathematics (2009) A long-standing conjecture states that if A is a finite group acting fixed point freely on a finite solvable group G of order coprime to jAj, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. If A is nilpotent, it is expected that the conjecture is true without the coprimeness condition. We prove that the conjecture without the coprimeness condition is true when A is a cyclic group whose order is a product of three primes which are coprime to 6 and the Sylow 2-sub...
Studies on the perturbation problems in quantum mechanics Koca, Burcu; Taşeli, Hasan; Department of Mathematics (2004) In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schrodinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.
Smooth manifolds with infinite fundamental group admitting no real projective structure Çoban, Hatice; Ozan, Yıldıray; Department of Mathematics (2017) In this thesis, we construct smooth manifolds with the infinite fundamental group Z_2*Z_2, for any dimension n>=4, admitting no real projective structure. They are first examples of manifolds in higher dimensions with infinite fundamental group admitting no real projective structures. The motivation of our study is the related work of Cooper and Goldman. They proved that RP^3#RP^3 does not admit any real projective structure and this is the first known example in dimension 3.

Citation Formats

R. Turhan, “Integrable nonautonomous KdV systems,” Ph.D. - Doctoral Program, Middle East Technical University, 2002.