New exact multi line soliton and periodic solutions with constant asymptotic values at infinity of the NVN integrable nonlinear evolution equation via dibar-dressing method
Abstract
The classes of exact multi line soliton, periodic solutions and solutions with functional parameters, with constant asymptotic values at infinity u|xi2+eta2->infty->-epsilon, for the hyperbolic and elliptic versions of the Nizhnik-Veselov-Novikov (NVN) equation via dibar-dressing method of Zakharov and Manakov were constructed. At fixed time these solutions are exactly solvable potentials correspondingly for one-dimensional perturbed telegraph and two-dimensional stationary Schroedinger equations. Physical meaning of stationary states of quantum particle in exact one line and two line soliton potential valleys was discussed. In the limit epsilon->0 exact special solutions u1, u2 (line solitons and periodic solutions) were found which sum u1+u2(linear superposition) is also exact solution of NVN equation.