An integrable semi-discretization of the Boussinesq equation

作者：Zhang, Yingnan; Tian, Lixin^*

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2016, 380(43): 3575-3582.

DOI：10.1016/j.physleta.2016.09.003

• Boussinesq equation
• Integrable discretization
• Soliton solutions
• Numerical simulation

In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the 'time' variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Backlund transformation and a Lax pair of the differential-difference system. For the case of 'good' Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

• 出版日期2016-10-23
• 单位江苏大学; 南京师范大学