Nonlocal symmetries, consistent tanh expansion solvability and interaction solutions for a new fifth-order nonlinear integrable equation

ABSTRACT

The nonlocal symmetries for a new fifth-order integrable equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables and the corresponding finite transformations are computed directly. New exact solutions of the new fifth-order integrable equation are also proved to have the consistent tanh expansion form. New exact interaction excitations such as soliton–cnoidal wave solutions and soliton–periodic wave solutions are given out analytically and graphically.

KEYWORDS:

• Nonlocal symmetry
• consistent tanh expansion method
• soliton–cnoidal waves
• new fifth-order nonlinear equation

PACS NUMBERS:

• 02.30.Jr
• 02.30.Ik
• 05.45.Yv

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by National Natural Science Foundation of China (No. 11471215), Shanghai Natural Science Foundation (No. 18ZR1426600) and the Hujiang Foundation of China (B14005).