New Representations of Multiperiodic and Multisoliton Solutions for a Class of Nonlocal Soliton Equations

Abstract

We present the new representations of the multiperiodic and multisoliton solutions of the Benjamin–Ono and nonlocal nonlinear Schrodinger equations. The key idea in the analysis is to explore the structure of the determinantal expressions of the solutions. After providing a direct verification of the multiperiodic solution by means of an elementary theory of determinants, we show that the solution admits a representation in terms of solutions for a system of nonlinear algebraic equations. This representation is found to be an analog of the multiperiodic solution of the Korteweg–de Vries equation. We also discuss the long-wave limit of the results associated with the multiperiodic solutions.