Abstract
The generalized Boussinesq equation is a useful model to describe the water wave. In this paper, with the coupled Alice-Bob (AB) systems, the nonlocal Boussinesq system can be obtained via the parity and time reversal symmetry reduction. By introducing an extended Bäcklund transformation, the symmetry breaking rogue wave, symmetry breaking soliton and symmetry breaking breather solutions for a nonlocal Boussinesq system are obtained through the derived Hirota bilinear form. The residual symmetry and finite symmetry transformation of the nonlocal AB-Boussinesq system are also studied.
Highlights
By introducing an extended Bäcklund transformation, the symmetry breaking rogue wave, symmetry breaking soliton and symmetry breaking breather solutions for a nonlocal Boussinesq system are obtained through the derived Hirota bilinear form
By using the Darboux transformation, some types of shifted parity and time reversal symmetry breaking solutions, including such localized structures as one-soliton, two-soliton, and rogue wave solutions were explicitly depicted for the AB-mKdV system[7]
We studied the nonlocal Boussinesq equation coupled with AB systems
Summary
By introducing an extended Bäcklund transformation, the symmetry breaking rogue wave, symmetry breaking soliton and symmetry breaking breather solutions for a nonlocal Boussinesq system are obtained through the derived Hirota bilinear form. By using the Darboux transformation, some types of shifted parity and time reversal symmetry breaking solutions, including such localized structures as one-soliton, two-soliton, and rogue wave solutions were explicitly depicted for the AB-mKdV system[7]. Soliton and breather solutions of the AB-Boussinesq system
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