Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

We solve a spectral and an inverse spectral problem arising in the computation of peakon
solutions to the two-component PDE derived by Geng and Xue as a generalization of the …

The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (NLS) equation on
the half-plane with nonzero boundary data is studied by advancing a novel approach …

It has been shown that the Cauchy problem for the Fokas–Olver–Rosenau–Qiao equation is
well-posed for initial data u_0 ∈ H^ su 0∈ H s, s> 5/2 s> 5/2, with its data-to-solution map …

In this paper, we show that the Fornberg–Whitham equation is Well-posed in Sobolev
spaces H s, for s> 3/2, and in the periodic case. We then show that the Well-posedness is …

In this paper, we consider the modified Camassa–Holm equation of the form y_t+ 2 u_x y+
uy_x= 0,\quad y=(1-\partial_x^ 2)^ 2 u. yt+ 2 uxy+ uyx= 0, y=(1-∂ x 2) 2 u. We prove that the …

We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By
interpreting this equation as a special case of a two-component peakon system (exhibiting a …

The initial value problem for a novel 4-parameter family of evolution equations, which are
nonlinear and nonlocal and possess peakon traveling wave solutions, is studied on both the …

Considered herein is the initial value problem for the two-component Novikov system with
peakons. Based on the local well-posedness results for this problem, it is shown that the …

In this paper, we study a fifth-order b-family Novikov (FObFN) model. Firstly, we establish the
local well-posedness and blow-up phenomena for the FObFN model. Secondly, we prove …