| Code |
Course Name |
Language |
Type |
| MAT 468E |
Nonlinear Waves |
English |
Elective |
| Local Credits |
ECTS |
Theoretical |
Tutorial |
Laboratory |
| 3 |
6 |
3 |
0 |
0 |
| Course Prerequisites and Class Restriction |
| Prerequisites |
MAT 331 MIN DD
or MAT 331E MIN DD
or MAT 234 MIN DD
or MAT 234E MIN DD
|
| Class Restriction |
None |
| Course Description |
| Korteweg-de Vries i.e. KdV equation; linear wave equation, superposition of solutions. Linear dispersive wave equation,
dispersion. The simplest nonlinear wave equation and discontinuous solutions. The balance between nonlinearity and
dispersion, and the KdV equation. Elementary solutions of the KdV equation; the qualitative behaviours of the traveling wave
solutions of the KdV equation. Description of solutions in terms of the Jacobian elliptic functions. Limiting behaviours of the
cnoidal wave and the solitary wave solutions.The scattering and inverse scattering problems; the scattering problem, the
inverse scattering problem, the solution of the Marchenko equation.The initial-value problem for the KdV equation.
Construction of the solution, Solitary wave and two-soliton solutions. Further properties of the KdV equation; Conservation
laws, Lax formulation and its KdV hierarchy, Hirota’s method, bilinear form of the KdV equation. Backlund transformations for
the KdV equation. The Painleve property of the KdV equations and numerical methods for the soliton solutions. |
|
