Exact explicit nonlinear wave solutions to a modified cKdV equation

Abundant explicit periodic wave solutions and their limit forms to space‐time fractional Drinfel'd–Sokolov–Wilson equation

“…In addition, note that if v(x, t) = v( ) is a solution of system (9), then v(x, t) = v( + ) is also a solution of system (9). Specially, taking = 2 , we obtain another two solutions (30). Furthermore, note that − 2 < 0 < 2 , and the component v(x, t) in (27) satisfies v(x, t) ∈ (− 2 , 2 ).…”

“…However, one may wander whether there exist other types of solution, such as periodic wave solutions, and how about their relation with other solutions. If so, can we find the M/W-shaped periodic wave solutions to Equation (1) (in fact, W-shaped periodic wave solutions has been found in other equations 29,30 ), since there exist M/W-shaped solitary wave solutions. Motivated by these problems, in this paper, we further study periodic wave solutions to Equation (1).…”

Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis

“…However, for methods starting from some assumed solutions and working out how to satisfy the NDE analytically as an inverse problem, there are many successes. Some of these inverse examples include the inverse differential and integral methods such as, for wave propagation [1], the G'/G expansion method [2] and its various variants [3][4][5], and inverse scattering methods for antenna design [6]. Generally, as an inverse problem, there is no limit to how many solutions can be found because there are an infinite number of choices for the set of system parameters that define the chosen base functions.…”

New approaches for periodic wave solutions of a non-Newtonian filtration equation with variable delay

“…After that, more related papers for non-Newtonian filtration equation and related nonlinear equation appeared, see e.g. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”