# Korteweg-de Vries Field Equations - Natalija 1b05ub05

Structure of Mathematics.

The Korteweg-de Vries equation.

Solution of the Korteweg-de Vries equation.

Derivation of conservation laws.

Numerical solution of the Korteweg-de Vries equation.

Equations of motion.

Lagrange formulation of field equations.

Nonlinear field equations.

Soliton solutions of the Korteweg-de Vries equation.

Conservation laws of the Korteweg-de Vries equation.

Motion in the central force field.

Light bending in the gravitational field.

Einstein's field equations (vacuum case).

Examples for metric tensors.

Einstein's field equations.

The Brachistochrone problem.

Lagrangian depending on a set of variables.

Potential and electric fields of discrete charge distributions.

Boundary problem of electrostatics.

Two ions in the Penning trap.

The orbits in general relativity.

Interactive use of Mathematics.

The mechanics of discrete systems.

Two coupled harmonic oscillators.

Solutions for different values of energy.

The damped driven pendulum.

Cartesian space in cylindrical coordinates.

Euclidean Space in polar coordinates.

The Schwarzschild solution.

The Schwarzschild metric in Eddington-Finkelstein form.

Schwarzschild metric in Kruskal coordinates.

The Reissner-Nordstrom solution for a charged.

Multi-fractals with common scaling factor.

The renormalization group.

bibliographies

# Korteweg-de Vries Field Equations - Natalija 1b05ub05