1.School of Mathematics Science, Xuzhou Normal University, Xuzhou 221116, China
;2.Department of Mathematics, Shanghai University, Shanghai 200444, China
Abstract:
In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Schrödinger equation can be a summation of squares of wave functions from bilinear point of view.