A class of super integrable Korteweg-de Vries systems

Dağ, Hüseyin


Energy preserving methods for korteweg de vries type equations
Şimşek, Görkem; Karasözen, Bülent; Aydın, Ayhan; Department of Scientific Computing (2011)
Two well-known types of water waves are shallow water waves and the solitary waves. The former waves are those waves which have larger wavelength than the local water depth and the latter waves are used for the ones which retain their shape and speed after colliding with each other. The most well known of the latter waves are Korteweg de Vries (KdV) equations, which are widely used in many branches of physics and engineering. These equations are nonlinear long waves and mathematically represented by partial...
An evolution operator approach for solving initial value problems
Ergenç, Tanıl; Çelebi, Okay; Demiralp, Metin; Department of Mathematics (1988)
A probabilistic design approach for rock slopes
DUZGUN, HSB; Karpuz, Celal; Yücemen, Mehmet Semih (1998-10-09)
The basic aim of this study is to develop a reliability-based methodology for the practical design of rock slopes. The advanced first-order second-moment (AFOSM) approach is adapted as;the reliability assessment model. In the reliability-based design methodology, the first step is the modeling and quantification of uncertainties associated with the design parameters. Since the safety of a rock slope is most sensitive to the shear strength of discontinuities, the uncertainty analysis is focused on the parame...
Multisymplectic Schemes for the Complex Modified Korteweg-de Vries Equation
AYDIN, AYHAN; Karasözen, Bülent (2008-09-20)
In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.
A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms
Yücel, Hamdullah; BENNER, Peter (2015-11-01)
In this paper, we study the numerical solution of optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms, arising from chemical processes. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used as a discretization method. We use a residual-based error estimator for the state and the adjoint variables. An adaptive mesh refinement indicated by a posteriori error estimates is applied. The arising saddle point system...
Citation Formats
H. Dağ, “A class of super integrable Korteweg-de Vries systems ,” M.S. - Master of Science, Middle East Technical University, 2003.