General Rational Solutions and Soliton Solutions of the Nonlocal Resonant Nonlinear Schrodinger Equations

Abstract

General rational solutions for the nonlocal resonant nonlinear Schrodinger equations are derived by using the Hirota bilinear method and the KP hierarchy reduction method. These rational solutions are presented in terms of determinants in which the elements are algebraic expressions. A weaker condition is given for KP reduction in the nonlocal case. The dynamics of first-order solutions are investigated in details. As a special case, we studied rantional solutions of the RNLS equation. Moreover, soliton solutions of the RNLS equation are given by using the Backlund transformation and nonlinear superposition formula.