Multi-peakons, lumps, and other solitons solutions for the ($$\varvec{2+1}$$)-dimensional generalized Benjamin–Ono equation: an inverse $$\varvec{(G'/G)}$$-expansion method and real-world applications

Exploring cone-shaped solitons, breather, and lump-forms solutions using the lie symmetry method and unified approach to a coupled breaking soliton model

“…The ability to solve these equations analytically has gained paramount importance. Numerous methods have been developed by researchers and scholars to extract solutions for different types of NLPDEs [1][2][3]. These methods include the Painlevé test [4], the F-expansion method [5], the Lie symmetry method [6,7], the Bell polynomial method [8], the generalized exponential rational function method [9], the generalized Riccati equation mapping method [10], the Hirota bilinear method [11], the Backlund transformation [12], the Exp-function method [13], geometric approach [14], the extended tanh-coth expansion method [15], the Extended Sinh-Gordon equation method [16], the extended trial equation scheme [17], the Darboux transformation method [18,19], the generalized perturbation (n, N − n)-fold Darboux transformation [20], the Extended rational sin-cos method [21] and many more [22].…”