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 togethe...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 nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq 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.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51579040,51379033,and 51522902)the National Basic Research Program of China(Grant No.2013CB036101)Liaoning Natural Science Foundation,China(Grant No.201602172)
文摘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 nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq 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.
