Multi–solitons, lumps, and breath solutions of the water wave propagation with surface tension via four recent computational schemes

This research explores the complex and physical behavior, using four different theoretical methods, of water wave propagation with surface tension. A modern Benneye-Luke (BL) algorithm is used to identify a variety of unobtained distinct wave solution forms, such as multi-solitons, lumps and breath-solutions by modified Khater (MK) method, improved Riccati expansion (IRE) method, novel [Formula presented] expansion (NGE) method, and generalized Kudryashov (GK) method. The nature of the Hamiltonian method often discusses the properties of the model form. Furthermore, some of the solutions in various forms of plots can be clarified by the complex actions of water wave propagation.