The purpose of this paper is to establish a new method for proving the conver-gence of the particle method applied to the Camassa-Holm (CH) equation. The CH equation is a strongly nonlinear, bi-Hamiltonian, completely integrable model in the context of shallow water waves. The equation admits solutions that are nonlinear su-perpositions of traveling waves that have a discontinuity in the first derivative at their peaks and therefore are called peakons. This behavior admits several diverse scientific applications, but introduce difficult numerical challenges. To accurately capture these solutions, one may apply the particle method to the CH equation. Using the concept of space-time bounded variation, we show that the particle solution conver...
This paper is devoted to the continuation of solutions to the Camassa-Holm equation after wave break...
The interest in the Camassa-Holm equation inspired the search for various generalizations of this eq...
ABSTRACT. We consider the Camassa-Holm equation with data in the energy norm H 1(R1). Global solutio...
We present a new self-contained convergence analysis of the particle method that can be applied to a...
The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics ...
In this paper we prove rigorously that in the long-wave limit the unidirectional solutions of the im...
Abstract. The purpose of this paper is to provide global existence and uniqueness results for a fami...
The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) sha...
The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics ...
The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) sh...
This paper develops a new approach in the analysis of the Camassa-Holm equation. By introducing a ne...
In this paper we employ two recent analytical approaches to investigate the possible classes of trav...
In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type e...
In this paper we employ two recent analytical approaches to investigate the possible classes of trav...
In this paper we employ two recent analytical approaches to investigate the possible classes of trav...
This paper is devoted to the continuation of solutions to the Camassa-Holm equation after wave break...
The interest in the Camassa-Holm equation inspired the search for various generalizations of this eq...
ABSTRACT. We consider the Camassa-Holm equation with data in the energy norm H 1(R1). Global solutio...
We present a new self-contained convergence analysis of the particle method that can be applied to a...
The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics ...
In this paper we prove rigorously that in the long-wave limit the unidirectional solutions of the im...
Abstract. The purpose of this paper is to provide global existence and uniqueness results for a fami...
The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) sha...
The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics ...
The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) sh...
This paper develops a new approach in the analysis of the Camassa-Holm equation. By introducing a ne...
In this paper we employ two recent analytical approaches to investigate the possible classes of trav...
In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type e...
In this paper we employ two recent analytical approaches to investigate the possible classes of trav...
In this paper we employ two recent analytical approaches to investigate the possible classes of trav...
This paper is devoted to the continuation of solutions to the Camassa-Holm equation after wave break...
The interest in the Camassa-Holm equation inspired the search for various generalizations of this eq...
ABSTRACT. We consider the Camassa-Holm equation with data in the energy norm H 1(R1). Global solutio...