Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation

• 来源期刊: 中国物理B（英文版）
• 关键词: nonlocal Boussinesq equation periodic wave solution solitary waves Riemann theta function
• 年，卷（期）: 2017,（5）
• 页码范围: 90-96
• 页数: 7页
• 语种: 英文
• DOI: 10.1088/1674-1056/26/5/050504

摘要

We construct the Hirota bilinear form of the nonlocal Boussinesq (nlBq) equation with four arbitrary constants for the first time.It is special because one arbitrary constant appears with a bilinear operator together in a product form.A straightforward method is presented to construct quasiperiodic wave solutions of the nlBq equation in terms of Riemann theta functions.Due to the specific dispersion relation of the nlBq equation,relations among the characteristic parameters are nonlinear,then the linear method does not work for them.We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series.In fact,the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given.The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.