New three-wave solutions for the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abundant exact analytical solutions and novel interaction phenomena of the generalized (3+1)-dimensional shallow water equation

“…So far, several effective methods have been established by mathematicians and physicists to obtain exact solutions of NLEEs [1][2][3][4][5][6][7][8]. By using these methods, researchers constructed the exact solutions of NLEEs, such as soliton [9], rogue wave [10], breathers [11], periodic wave [12], three-wave solution [13], rational solutions [14], lump solution [15] and interaction solutions [16]- [18], etc.…”

Breather wave and lump‐type solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

“…Tang and Zai 4 obtained the new periodic‐wave solutions. Liu et al 5,6 given the new three‐wave and non‐traveling wave solutions. Mabrouk and Rashed 7 obtained some new analytical solutions.…”

New Interaction Solutions for a (2 + 1)-Dimensional Vakhnenko Equation

“…Some 1-loop, 2-loop, and 3-loop soliton solutions were presented applying the improved Hirota method, and the traveling and interaction processes for the N-loop soliton solutions are explored in [25]. In this paper, we investigate interaction solutions of equation 1via Hirota's transformation [26] and three-wave methods [27][28][29][30]. 1Under the transformation W � 6(lnf) X , equation 4becomes the Hirota bilinear equation:…”