The role of magnetic fields for curvature effects in Josephson junction

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

“…Based on the ansatz methods devised, we have constructed bright and dark soliton solutions for the fractional Sawada-Kotera equation in Eqs. (17) and (21); singular soliton solutions for the fractional Caudrey-Dodd-Gibbon in equations (25) and (29); bright and dark soliton solutions for the fractional Lax equation in Eqs. (33) and (37); exponential solutions for the fractional Kaup-Kuperschmidt in Eqs.…”

“…Since the discovery of the soliton in 1965 by Zabusky and Kruskal [6], many nonlinear PDEs have been derived and extensively applied in different branches of physics and applied mathematics [7][8][9][10][11][12][13][14][15][16][17]. Nonlinear PDEs appear in condensed matter, solid state physics, fluid mechanics, chemical kinetics, plasma physics, nonlinear optics, propagation of fluxion in Josephson junctions, ocean dynamics and many others [18][19][20][21][22][23][24][25][26][27]. In order to understand the different nonlinear phenomena, various methods for obtaining exact solutions to nonlinear PDEs have been proposed [28][29][30][31].…”