New explicit and exact solutions for the Nizhnik-Novikov-Vesselov equation. (English) Zbl 0996.35066
Summary: Several explicit and exact travelling wave solutions for the Nizhnik-Novikov-Vesselov equation
\[
u_t=au_{xxx}+ bu_{yyy}-3av_xu-3 avu_x-3b\omega_yu- 3b\omega u_y,
\]
\[ u_x=v_y,\;u_y=\omega_x, \] are obtained by using the hyperbola function method and the Wu-elimination method, which include new singular solitary wave solutions and periodic solutions.
\[ u_x=v_y,\;u_y=\omega_x, \] are obtained by using the hyperbola function method and the Wu-elimination method, which include new singular solitary wave solutions and periodic solutions.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 35C05 | Solutions to PDEs in closed form |
| 35Q51 | Soliton equations |
