Solitons on a background, rogue waves, and classical soliton solutions of extended Nonlinear Schrödinger Equations

For short pulses with wide spectrum, the Nonlinear Schrödinger Equation (NLS) has to be supplemented with additional terms that describe higher-order effects. If the coefficients are related in a special way, analytic solutions can be found, as, e.g., for the Hirota Equation and the Sasa-Satsuma equation (SSE). We concentrate on the SSE, where soliton solutions, and, more recently, heteroclinic connections have been presented [1]. We will consider the most general case of a soliton on a background solution and demonstrate several limiting cases. Among these limits are rogue waves and classical solitons with zero background.