Abstract:
Explicit examples are constructed of two-dimensional rational potentials that decrease at infinity and are reflectionless for given energy. It is shown that these potentials correspond to soliton solutions of the (2+1)-dimensional nonlinear equations found by Veselov and Novikov.
Citation:
P. G. Grinevich, “Rational solitons of the Veselov–Novikov equations are reflectionless two-dimensional potentials at fixed energy”, TMF, 69:2 (1986), 307–310; Theoret. and Math. Phys., 69:2 (1986), 1170–1172