Hyperelliptic function solutions of three genus for KP equation using direct method. (English) Zbl 1222.37057
Summary: We will use a simple and direct method to obtain some particular solutions of \((2+1)\)-dimensional and \((3+1)\)-dimensional KP equations expressed in terms of the Kleinian hyperelliptic functions for a given curve \(y^2=f(x)\) whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 33E05 | Elliptic functions and integrals |
