We study the long time asymptotic behavior for the Cauchy problem of the modified
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …

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 …

The aim of this paper is to develop an analytical approach to obtain the sharp estimates for
the lowest positive periodic eigenvalue and all Dirichlet eigenvalues of a general Sturm …

In this paper, we present a short proof of the maximization of Dirichlet eigenvalue ratios for
the Camassa–Holm equation y′′= 1 4 y+ λ m (x) y, by solving the infinitely dimensional …

MINIMIZATION OF LOWEST POSITIVE PERIODIC EIGENVALUE FOR CAMASSA-HOLM
EQUATION WITH INDEFINITE POTENTIAL 1. Introduction It is we Page 1 MINIMIZATION OF …

This article is concerned with the isospectral problem− f ″+ 1 4 f= z ω f+ z 2 υ f for the
periodic conservative Camassa–Holm flow, where ω is a periodic real distribution in H loc …

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 extend the inverse spectral transform for the conservative Camassa-Holm flow on the
line to a class of initial data that requires strong decay at one endpoint but only mild …

Based on the∂‾-generalization of the Deift-Zhou steepest descent method, we extend the
long-time and Painlevé asymptotics for the Camassa-Holm (CH) equation to the solutions …

For the classical Sturm-Liouville operators, we prove the sharp bounds for all nodes of
eigenfunctions by regarding these nodes as nonlinear functionals of potential q∈ L1 [0, 1] …