Lump solutions to dimensionally reduced $$\varvec{p}$$ p -gKP and $$\varvec{p}$$ p -gBKP equations

Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

“…Compared with the rogue wave, lump solution is a special kind of solution, rationally localized in all directions in the space. So the lump solution has also attracted more and more attention [10][11][12][13][14], and it can be studied through Hirota bilinear equation. One equation can be transformed into a new equation with Hirota bilinear method [15][16][17]; the new equation is called the Hirota equation.…”

“…One equation can be transformed into a new equation with Hirota bilinear method [15][16][17]; the new equation is called the Hirota equation. Some special examples of lump solutions have been found, such as KPI equation [12], p-gBKP equation [11], KdV equation [18], and Davey-Stewartson II equation [19,20]. More importantly, Zhang and Chen showed lump solution and its interaction phenomenon with a pair of stripe (line) solitons of a reduced (3+1)-dimensional Jimbo-Miwa equation [10].…”

Rogue wave and a pair of resonance stripe solitons to KP equation

“…Recently, Ma proposed the positive quadratic function to get the lump solution. Special examples of lump solutions have been found, such as the KPI equation [16,17,18], BKP equation [19],the p-gKP and p-gBKP equations [20], Boussinesq equation [21] and so on.…”

Bright and dark soliton solutions to the partial reverse space–time nonlocal Mel’nikov equation

“…A variety of powerful methods have been used to obtain solutions to NLLEs and to investigate the physical properties of these solutions. Examples of these methods include the Darboux transformation method [9,10], the inverse scattering method [11], the Hirota bilinear method [13], the homogeneous balance method [14,15], the Lie group method [16,17], the direct method [18,19,20], and so on [21,22,23].…”