New exact solutions for the classical Drinfel’d–Sokolov–Wilson equation

Bifurcation of peakons and periodic cusp waves for the generalization of the Camassa–Holm equation

“…In this paper, we employ the bifurcation method and qualitative theory of dynamical systems [3,4,8,9,[12][13][14]16,17] to investigate Eq. (1.4).…”

Bifurcations and nonlinear wave solutions for the generalized two-component integrable Dullin–Gottwald–Holm system

“…Han et al [9] studied the solitary waves and wave-breaking phenomena for GDGH2 system (2). In this paper, we study the bifurcations and nonlinear wave solutions for the GDGH2 system (2) by employing the bifurcation method and qualitative theory of dynamical systems [6,7,12,[14][15][16][17][18][19][20][22][23][24]. Through the bifurcations of phase portraits corresponding to system (2), we not only show the existence of several types of nonlinear wave solutions, including solitary waves, peakons, periodic cusp waves, periodic waves, compacton-like waves and kink-like waves, but also obtain their implicit expressions.…”

Q‐symmetry and conditional Q‐symmetries for Drinfel'd–Sokolov–Wilson system

“…In this paper, we are concerned with the classical Drinfel'd–Sokolov–Wilson (DSW) equation where p, q, r, and s are some nonzero parameters. Recently, DSWE and the coupled DSWE, a special case of the classical DSWE, have been studied by several authors ‐. In this study, we construct the Q‐symmetry and conditional Q‐symmetries of DSW equations.…”

“…where p, q, r, and s are some nonzero parameters. Recently, DSWE and the coupled DSWE, a special case of the classical DSWE, have been studied by several authors [13]- [14]. In this study, we construct the Q-symmetry and conditional Q-symmetries of DSW equations.…”