The Cauchy problem for a generalized Camassa–Holm equation

A Novikov equation describing pseudo‐spherical surfaces, its pseudo‐potentials, and local isometric immersions

“…Remark Depending on the initial data, Equation () admits analytic solutions defined on a strip of $$\mathbb {R}^2$$, see Ref. [18, Theorem 1.4]. As a consequence, we have granted the existence of analytic one‐forms () (with coefficients given by ()).…”

Well-posedness and behaviors of solutions to an integrable evolution equation

“…The behaviors of solutions to the CH equation with dissipative term and dispersion term are studied in [25]. The local well-posedness for the Cauchy problem of the CH type equations [6,15,20,26,[28][29][30][31], asymptotic stability [17,22], solitons solutions [14], and regularity of conservative solutions [18] are considered. The readers may refer to [8-10, 18, 20-22] Molinet [23] considers the peakon solutions of the DP equation.…”

The dynamic properties of solutions for a nonlinear shallow water equation

“…The properties of solutions to the problem with dispersion and dissipative terms are discovered in [15]. Mi et al [12] investigate the dynamical properties for a generalized CH equation. For a related study of the CH equation and other related partial differential equations, one may refer to references [3,7,11,14,16].…”