Abstract
In this paper, the solutions of a first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term and Fan's direct algebraic method of obtaining exact solution to nonlinear PDEs are applied to two nonlinear evolution equations, the combined KdV-MKdV equation and generalized Zakharov equations. As a result, some special exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, bright and dark solitary wave solutions, triangular periodic wave solutions and singular solutions.
| Original language | English |
|---|---|
| Pages (from-to) | 257-269 |
| Number of pages | 13 |
| Journal | Reports on Mathematical Physics |
| Volume | 57 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2006 |
| Externally published | Yes |
Keywords
- direct algebraic method
- exact travelling wave solutions
- nonlinear evolution equations
- solitary wave solutions