Single peak solitary wave solutions for the generalized KP–MEW (2,2) equation under boundary condition

Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

“…The solutions of (1) have been studied in various aspects. See, for example, the recent papers [26][27][28]. Wazwaz [26] used the tanh method and the sine-cosine method, for finding solitary waves and periodic solutions.…”

“…Saha [27] used the theory of bifurcations of planar dynamical systems to prove the existence of smooth and nonsmooth travelling wave solutions. Wei et al [28] used the qualitative theory of differential equations and obtained peakon, compacton, cuspons, loop soliton solutions, and smooth soliton solutions.…”

Peakon, Cuspon, Compacton, and Loop Solutions of a Three-Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion

“…Studies of various physical structures of nonlinear dispersive equations had attracted much attention in connection with the important problems that arise in scientific applications. Mathematically, these physical structures have been studied by using various powerful and efficient methods, such as inverse scattering method [1], Darboux transformation method [2,3], Hirota bilinear method [4], Lie group method [5,6], bifurcation method of dynamic systems [7,8], tanh function method [9][10][11][12], Fan-expansion method [13,14], and homogenous balance method [15]. Practically, there is no unified technique that can be employed to handle all types of nonlinear dispersive equations.…”

“…Systems (8) are planar dynamical systems defined in the 3-parameter space ( , , ). For a fixed , we will investigate the bifurcations of phase portraits of (8) in the phase plane ( , ) as the parameters , are changed.…”

Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal

“…under the inhomogeneous boundary condition and obtained smooth, peaked, cusped soliton solutions of the osmosis (2, 2) equation by using the phase portrait analytical technique. Wei et al [28] investigated the generalized KP-MEW(2,2) equation…”