N-solitons and cuspon waves solutions of (2 + 1)-dimensional Broer–Kaup–Kupershmidt equations via hidden symmetries of Lie optimal system

• Published in: Chinese journal of physics (Taipei) Vol. 57; pp. 90 - 104
• Main Authors: Kassem, M.M., Rashed, A.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2019
• Subjects: Hidden symmetries; Lie optimal system; System of partial differential equations; 76M60; Lie optimal system; 35Q53; System of partial differential equations; Hidden symmetries; 76B15
• ISSN: 0577-9073
• DOI: 10.1016/j.cjph.2018.12.007

•Broer–Kaup–Kupershmidt (BKK) quations have been investigated.•Optimal system of Lie vectors has been created.•Hidden symmetries have been discovered throughout reduction process to ODE.•Only hidden symmetries have been used to constuct new exact solutions.•The solutions include solitons and cuspon waves. Broer–Kaup–Kupershmidt (BKK) system of partial differential equations in (2 + 1)-dimensions has been investigated and new analytical solutions have benn attained by the aid of discovering hidden symmetries of Lie optimal system. The optimal system of Lie vectors is derived invoking commutator and adjoint tables. Thereafter, BKK system is reduced into a system of ordinary differential equations in two steps. At each step, hidden symmetries are detected. Such symmetries are those which not being inherited by the previous step. Only hidden symmetry vectors are exploited in attaining analytical solutions of BKK equation. Unlike ad-hoc methods, exponential function method and tanh-coth method etc., the solutions are attained throughout symmetry reductions procedures resulting in some new results including N-solitons and cuspon waves. The latter has a very sharp cusp along its crest and has been compred with previous work.