A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The
regularised equations are non-dissipative, non-dispersive and posses a variational …

Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been
introduced by Clamond and Dutykh (2018). This system is Galilean invariant, linearly non …

We have developed a new procedure for converting nonlinear third-order ordinary
differential equations into linear forms using point transformation. These linear equations are …

We study a class of partial differential equations (PDEs) in the family of the so‐called Euler–
Poincaré differential systems, with the aim of developing a foundation for numerical …

This thesis studies a regularization of the classical Saint-Venant (shallow-water) system,
namely the regularized shallow-water (Airy or Saint-Venant) system, recently introduced by …

We present a particle method for studying a quasilinear partial differential equation (PDE) in
a class proposed for the regularization of the Hopf (inviscid Burger) equation via nonlinear …

Physical details of the Camassa–Holm (CH) equation that are difficult to obtain in space-time
simulation can be explored by solving the Lax pair equations within the direct and inverse …

Journal of Nonlinear Mathematical Physics Page 1 Journalo f Nonline a Mathem ysics vol. 13
numbers 1-4, 2006 issn 1402-9251 Editor-in-Chief Prof. N. Euler, Luleå University of Technology …

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The
regularised equations are non-dissipative, non-dispersive and possess a variational …

We study centred second order in time and space finite difference methods of the inviscid
Burgers equation, deriving a more general numerical discretisation scheme, than the one …