On the solutions for an Ostrovsky type equation

Well-Posedness Results for the Continuum Spectrum Pulse Equation

“…Arguing as in ( [15], Lemma 2.2), we have (22), (23) and (24). Finally, arguing as in ( [6], Lemma 2.3), we have (25).…”

“…whose the well-posedness is studied in [15]. From a mathematical point of view, the presence of the term 3gu 2 ∂ x u − a∂ 3 x u in the first equation of (1) makes the analysis of such system more subtle than the one of (6). Observe that, taking b = α = β = 0, (1) becomes the modified Korteweg-de Vries equation (see [16][17][18][19][20])…”

“…In [8,9,[21][22][23][24], it is proven that (7) is a non-slowly-varying envelope approximation model that describes the physics of few-cycle-pulse optical solitons. In [6,18], the Cauchy problem for (7) is studied, while, in [16,19], the convergence of the solution of (7) to the unique entropy solution of the following scalar conservation law…”

“…Mathematical properties of (10) are studied in many different contexts, including the local and global well-posedness in energy spaces [43,53] and stability of solitary waves [53,54], while, in [6], the well-posedness of the classical solutions is proven.…”

On Classical Solutions for A Kuramoto–Sinelshchikov–Velarde-Type Equation

“…In this paper, we investigate the well-posedness of the following Cauchy problem: 3 + r(∂ x u) 4 + δ∂ 3 x u +β 2 ∂ 4…”