Application of extended rational trigonometric techniques to investigate solitary wave solutions

In this paper, a variety of novel exact traveling wave solutions are constructed for the $$(2+1)$$ -dimensional Boiti-Leon-Manna-Pempinelli equation via analytical techniques, namely, extended rational sine-cosine method and sinh-cosh method. The physical meaning geometrical structures some these is discussed. Obtained expressed in terms singular periodic wave, solitary waves, bright solitons, dark kink with specific values parameters. For observation activities problem, achieved vital. Moreover, to find proposed many methods have been used but given methodologies effective, reliable gave more solutions.