Global conservative solutions of the Camassa–Holm equation
A Bressan, A Constantin - Archive for Rational Mechanics and Analysis, 2007 - Springer
This paper develops a new approach in the analysis of the Camassa–Holm equation. By
introducing a new set of independent and dependent variables, the equation is transformed …
introducing a new set of independent and dependent variables, the equation is transformed …
Global dissipative solutions of the Camassa–Holm equation
A Bressan, A Constantin - Analysis and Applications, 2007 - World Scientific
This paper is devoted to the continuation of solutions to the Camassa–Holm equation after
wave breaking. By introducing a new set of independent and dependent variables, the …
wave breaking. By introducing a new set of independent and dependent variables, the …
[HTML][HTML] A view of the peakon world through the lens of approximation theory
H Lundmark, J Szmigielski - Physica D: Nonlinear Phenomena, 2022 - Elsevier
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 …
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …
Global conservative solutions of the Camassa–Holm equation—a Lagrangian point of view
We show that the Camassa–Holm equation ut− uxxt+ 3uux− 2uxuxx− uuxxx= 0 possesses a
global continuous semigroup of weak conservative solutions for initial data u| t= 0 in H1. The …
global continuous semigroup of weak conservative solutions for initial data u| t= 0 in H1. The …
[PDF][PDF] Dissipative solutions for the Camassa-Holm equation
We show that the Camassa–Holm equation ut− uxxt+ 3uux− 2uxuxx− uuxxx= 0 possesses a
global continuous semigroup of weak dissipative solutions for initial data u| t= 0 in H1. The …
global continuous semigroup of weak dissipative solutions for initial data u| t= 0 in H1. The …
A general family of multi-peakon equations and their properties
A general family of peakon equations is introduced, involving two arbitrary functions of the
wave amplitude and the wave gradient. This family contains all of the known breaking wave …
wave amplitude and the wave gradient. This family contains all of the known breaking wave …
Bäcklund transformations for the Camassa–Holm equation
The Bäcklund transformation (BT) for the Camassa–Holm (CH) equation is presented and
discussed. Unlike the vast majority of BTs studied in the past, for CH the transformation acts …
discussed. Unlike the vast majority of BTs studied in the past, for CH the transformation acts …
Global conservative multipeakon solutions of the Camassa–Holm equation
We show how to construct globally defined multipeakon solutions of the Camassa–Holm
equation. The construction includes in particular the case with peakon-antipeakon collisions …
equation. The construction includes in particular the case with peakon-antipeakon collisions …
The inverse spectral transform for the conservative Camassa–Holm flow with decaying initial data
J Eckhardt - Archive for Rational Mechanics and Analysis, 2017 - Springer
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 …
Data Page 1 Digital Object Identifier (DOI) 10.1007/s00205-016-1066-z Arch. Rational Mech …
The inverse spectral problem for indefinite strings
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 …
Holm equation), we introduce a new class of generalized indefinite strings associated with …