Abstract In this paper, the partially party‐time ( ) symmetric nonlocal Davey–Stewartson (DS) equations with respect to x is called ‐nonlocal DS equations, while a fully DSII equation equation. Three kinds of solutions, namely, breather, rational, and semirational solutions for these are derived by employing bilinear method. For usual (2 + 1)‐dimensional breathers periodic in direction localized y direction. Nonsingular rational lumps, composed breathers, line waves. equation, both...

Recently, Fokas presented a nonlocal Davey–Stewartson I (DSI) equation (Fokas 2016 Nonlinearity 29 319–24), which is two-spatial dimensional analogue of the nonlinear Schrödinger (NLS) (Ablowitz and Musslimani 2013 Phys. Rev. Lett. 110 064105), involving self-induced parity-time-symmetric potential. For this equation, high-order periodic line waves breathers are derived by employing bilinear method. The long wave limit these solutions yields two kinds fundamental rogue waves, namely,...

Abstract Resonant collisions among localized lumps and line solitons of the Kadomtsev–Petviashvili I (KP‐I) equation are studied. The KP‐I describes evolution weakly nonlinear, dispersive waves with slow transverse variations. Lumps can only exist for KP when signs derivative weak dispersion in propagation direction different, that is, regime. Collisions “integrable” equations normally elastic, wave shapes preserved except possibly phase shifts. For resonant collisions, mathematically shift...

Resonant collisions of lumps with periodic solitons the Kadomtsev–Petviashvili I equation are investigated in detail. The usual lump is a stable weakly localized two-dimensional soliton, which keeps its shape and velocity course evolution from t → −∞ to +∞. However, would become time as instantons, result two types resonant spatially (quasi-1D) soliton chains. These partly fully collisions. In former case, does not exist at −∞, but it suddenly emerges chain, keeping amplitude constant +∞; or...

Fokas system is the simplest (2+1)-dimensional extension of nonlinear Schrödinger equation (Eq. (2), Inverse Problems 10 (1994) L19-L22). By using bilinear transformation method, general rational solutions for are given explicitly in terms two order-N determinants τn (n = 0, 1) whose elements m(n)i,j 1; 1 ≤ i, j N) involved with order-ni and order-nj derivatives. When N 1, three kinds solution, i.e., fundamental lump rogue wave (RW) n1 higher-order solution ≥ 2, illustrated by explicit...

Breathers and rogue waves as exact solutions of the three-dimensional Kadomtsev—Petviashvili equation are obtained via bilinear transformation method. The breathers in three dimensions possess different dynamics planes, such growing decaying periodic line (x, y), z) (y, t) planes. Rogue localized time, theoretically a long wave limit with indefinitely larger periods. It is shown that profiles y) or plane, which arise from constant background then retreat back to same again.

Abstract The rational and semirational solutions in the Boussinesq equation are obtained by Hirota bilinear method long wave limit. It is shown that contain dark bright rogue waves, their typical dynamics analysed illustrated. possess a range of hybrid solutions, solitons demonstrated detail three-dimensional figures. Under certain parameter conditions, new kind consisted breathers discovered, which describes waves interacting with at same time.

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave–short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These describe interactions between various types solutions, including line rogue waves, lumps, breathers dark solitons. We only focus on dynamical behaviours lumps solitons in this paper. Our detailed study reveals two different excitation phenomena: fusion...

General dark solitons and mixed solutions consisting of breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing bilinear method. By introducing two differential operators, semi-rational rogue waves, generated. These given in terms determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general wave expressed rational functions. It is shown that fundamental (simplest) waves line waves. also...

Elastic collisions of solitons generally have a finite phase shift. When the shift has finitely large value, two vertices (2 + 1)-dimensional two-soliton are significantly separated due to shift, accompanied by formation local structure connecting V-shaped solitons. We define this as stem structure. This study systematically investigates localized structures between in asymmetric Nizhnik–Novikov–Veselov system. These structures, arising from quasi-resonant solitons, exhibit distinct features...

The general set of nonlocal M-component nonlinear Schrödinger (nonlocal M-NLS) equations obeying the PT-symmetry and featuring focusing, defocusing, mixed (focusing-defocusing) nonlinearities that has applications in optics settings, is considered. First, multisoliton solutions this M-NLS presence absence a background, particularly periodic line wave are constructed. Then, we study intriguing soliton collision dynamics as well interesting positon on zero background background. In particular,...