Exact solutions of \((2+1)\)-dimensional HNLS equation. (English) Zbl 1219.35280
Summary: We use the classical Lie group symmetry method to get the Lie point symmetries of the \((2+1)\)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and reduce the \((2+1)\)-dimensional HNLS equation to some \((1+1)\)-dimensional partial differential systems. Finally, many exact travelling solutions of the \((2+1)\)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
