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|_{xi^2+eta^2->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 u^{1}, u^{2} (line solitons and periodic solutions) were found which sum u^{1}+u^{2}(linear superposition) is also exact solution of NVN equation.

43 pages, 28 figures, 25 references More exactly specified and concretize all figures, captions and explanations for these figures. The number of figures changed from 36 (in old version) to 28 (in new version)