Propagation of isolated waves of coupled nonlinear (2 + 1)-dimensional Maccari System in plasma physics

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

“…Here, g, h, and η are defined by equation (12) with the parameters' relations (13), (14), and (15). The restricted conditions in equation (16) are to be able to form a lump wave and guarantee the regularity of the function f .…”

“…The study of integrable nonlinear systems has become a hot topic in wave propagations and mathematical physics. Integrable systems approximately describe the evolution of various waves in many physical settings, including shallowwater waves with weakly nonlinear restoring forces, pulse propagation in optical fibers and wave guides, long internal waves in a density-stratified ocean, and ion acoustic waves in plasma [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In the higher-dimensional extensions of integrable nonlinear wave equation, the (2+1)-dimensional KdV equation or the asymmetrical Nizhnik-Novikov-Veselov (ANNV) equation [17] u t + u xxx + 3 u∂ −1 y u x…”

“…Although these results can also be derived by Darboux transformation [47][48][49][50], modified extended mapping method [1], and direct algebraic method [2], the bilinear method is still a powerful tool for solving integrable systems. It is worth mentioning that Seadawy et al obtained some new exact solutions of many integrable systems by using various methods, such as extend simple equation method and the exp ðϕðξÞÞ expansion method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For the ANNV equation (1), the lump solutions, mixed lump-stripe solutions, and periodic lump solutions were presented in [19].…”

Classification of All Single Traveling Wave Solutions of Fractional Coupled Boussinesq Equations via the Complete Discrimination System Method

“…Among them, constructing the exact traveling wave solution of this kind of coupled system is a very important topic. Many meaningful methods have been proposed to solve the exact solutions of coupled systems, including Lie symmetry analysis [9], the method of dynamical systems [10,11], Fan subequation method [12], generalized Jacobi elliptic function expansion method [13], extended modified auxiliary equation mapping method [14], and extended modified auxiliary equation mapping method [15].…”

Pure Traveling Wave Solutions for Three Nonlinear Fractional Models

“…The interested readers can see more works in Refs. ( [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]). Inc and coworkers presented the new soliton structures to some time-fractional nonlinear differential equations with a conformable derivative via the Ricatti-Bernoulli sub-ODE method [51].…”