In this paper, we investigate the formation of singularities and the existence of peaked
traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The …

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the
following steps:(1) Lax representation [L, M]= 0;(2) construction of fundamental analytic …

The Inverse Spectral Transform for the Conservative Camassa–Holm Flow with Decaying Initial
Data Page 1 Digital Object Identifier (DOI) 10.1007/s00205-016-1066-z Arch. Rational Mech …

Motivated by the study of certain nonlinear wave equations (in particular, the Camassa–
Holm equation), we introduce a new class of generalized indefinite strings associated with …

In this paper, we report an interesting integrable equation that has both solitons and kink
solutions. The integrable equation we study is, which actually comes from the negative KdV …

Generalized indefinite strings provide a canonical model for self-adjoint operators with
simple spectrum (other classical models are Jacobi matrices, Krein strings and 2× 2 …

We examine a two dimensional fluid system consisting of a lower medium bounded
underneath by a flatbed and an upper medium with a free surface. The two media are …

We study the inverse problem for the so-called operators with energy depending potentials.
In particular, we study spectral operators with quadratic dependence on the spectral …

Wave breaking for a modified two-component Camassa–Holm system Page 1 J. Differential
Equations 252 (2012) 2759–2770 Contents lists available at SciVerse ScienceDirect Journal of …

In this manuscript, we study the well-posedness, blow-up scenario and global solution of a
two–component b–family equations in space H s-1, p (R)× H s, p (R), s> max {2, 3 2+ 1 p} …