Quasi-Periodic Structures Based on Symmetrical Lucas Function of (2+1)-Dimensional Modified Dispersive Water-Wave System

By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a (2+1)-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riccati equation that the symmetrical Lucas functions satisfy. From the variable separation solution and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated. (general)