30 citations · 66 across the 6 of their papers we have counts for
6 papers
Refined wave breaking for the generalized Fornberg-Whitham equation
Jean-Claude Saut, Yuexun Wang
This paper considers a class of non-local equations that are weakly dispersive perturbations of the inviscid Burgers equation, which includes the Fornberg-Whitham equation as a spe…
Refined wave breaking for the one-dimensional nonlinear shallow water equations
Pingchun Liu, Jean-Claude Saut, Shihan Sun +1
This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespa…
Wave breaking for the generalized Fornberg-Whitham equation
Jean-Claude Saut, Shihan Sun, Yuexun Wang +1
This paper aims to show that the Cauchy problem of the Burgers equation with a weakly dispersive perturbation involving the Bessel potential (generalization of the Fornberg-Whitham…
Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schrödinger equations
Jean-Claude Saut, Yuexun Wang
This paper concerns the modified fractional Korteweg-de Vries (modified fKdV) and nonlinear Schrödinger (modified fNLS) equations, with the dispersions |D|^α\partial_x and |D|^{α+1…
The wave breaking for Whitham-type equations revisited
Jean-Claude Saut, Yuexun Wang
We prove wave breaking (shock formation) for some Whitham-type equations which include the Burgers-Hilbert equation, the fractional Korteweg-de Vries equation, and the classical Wh…
Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity
Jean-Claude Saut, Yuexun Wang
We prove global existence and modified scattering for the solutions of the Cauchy problem to the fractional Korteweg-de Vries equation with cubic nonlinearity for small, smooth and…