Propagation of nonlinear complex waves for the coupled nonlinear Schrödinger Equations in two core optical fibers

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

“…Here, the rational and the exponential functions are responsible for the rational lump and the line solitary wave, respectively. Similar to the case of the purely rational lump, one needs to collect the coefficients of x, y, and t and exponential functions after substituting equation (12) into equation (3). Then, we have a set of algebraic equations with respect to the parameters a i ði = 1, 2,⋯,9Þ, k, and k i ði = 1, 2, 3Þ, which gives the parameters' relations as follows:…”

“…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].…”

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

“…However, they must be evaluated in terms nonlinear dynamics due to significant modulation of the wave amplitude originated from cumulative nonlinear interactions. Nonlinear Schrödinger (NLS) equation is a very common equation which is providing a canonical design of involucre dynamics of a quasi-monochromatic planar wave propagating in a weakly nonlinear dispersive medium when dissipative effects are insignificant [25,26,27].…”