Explicit solutions for a nonlinear model of financial derivatives
  Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving a nonlinear Black-Scholes equation. 
Ljudmila A. Bordag, Alina Z. Chmakova