Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning

L Wang, Z Yan - Physica D: Nonlinear Phenomena, 2021 - Elsevier
In the field of mathematical physics, there exist many physically interesting nonlinear
dispersive equations with peakon solutions, which are solitary waves with discontinuous first …

On the finite time blow-up for the high-order Camassa-Holm-Fokas-Olver-Rosenau-Qiao equations

S Yang, J Chen - Journal of Differential Equations, 2024 - Elsevier
In this paper, we are concerned with the finite time blow-up for the high-order Camassa-
Holm-Fokas-Olver-Rosenau-Qiao equations, which is a generalization of the Camassa …

Growth of perturbations to the peaked periodic waves in the Camassa--Holm equation

A Madiyeva, DE Pelinovsky - SIAM Journal on Mathematical Analysis, 2021 - SIAM
Peaked periodic waves in the Camassa--Holm equation are revisited. Linearized evolution
equations are derived for perturbations to the peaked periodic waves, and linearized …

Blow-up data for a two-component Camassa-Holm system with high order nonlinearity

Z Wang, K Yan - Journal of Differential Equations, 2023 - Elsevier
This paper is concerned with the Cauchy problem for a two-component Camassa-Holm
system with high order nonlinearity, which is a multi-component extension of the Fokas …

Roadmap of the Multiplier Method for Partial Differential Equations

JA Alvarez-Valdez, G Fernandez-Anaya - Mathematics, 2023 - mdpi.com
This review paper gives an overview of the method of multipliers for partial differential
equations (PDEs). This method has made possible a lot of solutions to PDEs that are of …

[PDF][PDF] Peakon and cuspon solutions of a generalized Camassa-Holm-Novikov equation

L Zhang, Y Wang, C Khalique, Y Bai - system, 2018 - pdfs.semanticscholar.org
The bounded traveling wave solutions of a generalized Camassa-Holm-Novikov equation
with p= 2 and p= 3 are derived via the dynamical system approach. The singular wave …

The stability of the b-family of peakon equations

EG Charalampidis, R Parker, PG Kevrekidis… - …, 2023 - iopscience.iop.org
In the present work we revisit the b-family model of peakon equations, containing as special
cases the b= 2 (Camassa–Holm) and b= 3 (Degasperis–Procesi) integrable examples. We …

Stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation

A Chen, T Deng, Z Qiao - Monatshefte für Mathematik, 2022 - Springer
In this paper, we study the orbital stability of peakons and periodic peakons for a nonlinear
quartic Camassa-Holm equation. We first verify that the QCHE has global peakon and …

Orbital stability of periodic peakons for the generalized modified Camassa-Holm equation

B Moon - Discrete and Continuous Dynamical Systems-S, 2021 - aimsciences.org
This paper is devoted to studying the dynamical stability of periodic peaked solitary waves
for the generalized modified Camassa-Holm equation. The equation is a generalization of …

Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation

SC Anco, D Kraus - arXiv preprint arXiv:1708.02520, 2017 - arxiv.org
The modified Camassa-Holm (mCH) equation is a bi-Hamiltonian system possessing $ N $-
peakon weak solutions, for all $ N\geq 1$, in the setting of an integral formulation which is …