Explicit and implicit solutions of a generalized Camassa–Holm Kadomtsev–Petviashvili equation

Exact traveling wave solutions of a KPI equation

“…Sinelshchikov [3] demonstrate that four solutions from 13 of the KPI obtained by Khalfallah [2] are wrong and do not satisfy the equation. In this paper, we employ the method of dynamical systems [4][5][6][7] to investigate the traveling waves of the KPI.…”

Exact solutions of the 2+1-dimensional Camassa–Holm Kadomtsev–Petviashvili equation

“…By transformations (34) and (35), Eqs. (8) and (9) are converted respectively into the following ordinary differential equations:…”

“…It is well known that nonlinear evolution equations (NLEEs) are often presented to describe the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamics, plasma physics, nonlinear optics, etc. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The investigation of exact solutions of NLEEs is therefore an important area of research in this area.…”

Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms

“…According to the Hamiltonian, we can get all kinds of phase portraits in the parametric space. Because the phase orbits defined the vector fields of system (10) and determined all their travelling wave solutions of (3), by investigating the bifurcations of phase portraits of system (10), we can seek the travelling wave solutions of (3) [5][6][7][8][9][10][11]. The detailed calculation procedure can be found in the technical appendix.…”