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In this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect. We have also shown that DP-KP equation possesses periodic shock waves similar to that of the Degasperis-Procesi equation.

The rotation μ -Camassa–Holm equation (R- μ -CH) equation is a nonlinear partial differential equation closely related to the rotation Camassa–Holm (R-CH) equation (Chen et al., 2018; Gui et al., 2019a; Gui et al., 2019b; Tu et al., 2019). We prove that the nonexistence of the periodic peaked traveling wave solutions of the R- μ -CH equation unlike μ -CH equation. [ABSTRACT FROM AUTHOR]

Abstract: The existence of solitary wave solutions of the generalized two-component Hunter–Saxton system is determined. It is also shown that there are peaked and cusped solitary waves with singularities among those smooth solitary wave solutions. [Copyright &y& Elsevier]

Recently, Zhu et al. (2020) proposed a kind of rotation-Camassa–Holm equation. In this paper, we study the question of nonexistence of periodic peaked traveling wave solution for rotation-Camassa–Holm equation. Indeed, rotation-Camassa–Holm equation has no nontrivial periodic Camassa–Holm peaked solution unlike Camassa–Holm equation, modified Camassa–Holm equation, Novikov equation. [ABSTRACT FROM AUTHOR]