New double Wronskian exact solutions for a generalized (2+1)-dimensional nonlinear system with variable coefficients

Abundant Bounded and Unbounded Solitary, Periodic, Rogue‐Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model

“…But, this method initially bifurcated the phase orbits, and different types of orbits provided different types of solutions. e solutions (33), (35), (40), and (41) are consistent with homoclinic orbits and exhibit bell wave solutions, but (34) and ( 40) yield dark bell, while (36) and ( 41) yield bright bell wave envelops.…”

“…We merge the first equation of ( 29) and (35) with integration; we attain a valley-type smooth solitary wave solution…”

“…Rogue wave solutions are investigated in the coupled nonlinear Schrödinger models by Degasperis [31], while Ankiewicz found rogue signal elucidations of integrable nonlinear Schrödinger hierarchy [32]. Due to the sensitive effect of a rogue wave, scholars are being highly interested in deriving rogue and such type of colliding wave solutions in the recent exploration [33][34][35][36]. Moreover, dynamical researchers have investigated new rogon waves [37], optical M-shaped solitons with interaction with shock waves [38], orbital stability of solitary waves [39], and the nonexistence of global solutions of the time-fractional model [40] newly.…”

Interactions of rogue and solitary wave solutions to the (2 + 1)-D generalized Camassa–Holm–KP equation

“…Rogue waves are confined in mutually space as well as time, arise from nowhere even vanish lacking a trace [29][30][31][32], have engaged with the liability of abundant oceanic disasters. More complicated phenomena and effects of nonlinearities can be described from multi-soliton solutions of NLPDEs [33,34] using complex values to the free parameters involving in the multi-wave soliton solutions of the models [35,36]. Recently, enormous efforts have been salaried on diverge nonlinear models to derive collision among solitons, lump, rogue and hybrid solutions by dynamical researchers [37][38][39].…”

Dynamical interaction of solitary, periodic, rogue type wave solutions and multi-soliton solutions of the nonlinear models

“…Many scientific experimental models are employed in nonlinear differential equations (NLDEs) form including nonlinear fibers optics large-amplitude wave motions, fluids, plasma, solid-state physics etc. therefore, in the previous several times, many scientists and researchers worked to discover new effective methods [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] for explaining (NLDEs) which are significant to elucidate different intricate problem such as F-expansion method and exp-expansion method [1] , modified (g′/g)-expansion method [2] , improved differential transform method [3] , modified double sub-equation method [4] , extended (g′/g)-expansion method [5] , generalized (g′/g)-expansion method [6] , new generalized (g′/g)-expansion method [7] , discrete algebraic framework [8] , modified simple equation method [9] , hirota differential operator scheme [10] , IRM-CG method [11] , tanh method [12] , tanh and the sine–cosine methods [13] , hirota bilinear [14] , [15] , [16] , EMSE method [17] , generalized Riccati equation mapping method [18] , nonlinear capacity method [19] and so on.…”