Abstract In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as result reduction of order computing conservation laws are presented. Furthermore, μ -symmetry -conservation obtained.

A reciprocal transformation is introduced for a three-component Camassa-Holm type equation and it showed that the transformed system reduction of first negative flow in generalized MKdV hierarchy.

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the secondand third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of alg...

We study centred second-order in time and space discretizations of the inviscid Burgers equation. Although this equation in its continuum formulation supports non-smooth shock wave solutions, the discrete equation generically supports smooth solitary wave solutions. Using backward error analysis we derive the modified equation associated with the numerical scheme. We identify three different eq...

We study an equation lying ‘mid-way’ between the periodic HunterSaxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler equation on the diffeomorphism group of the circle corresponding to a natural right-invariant Sobolev metric. We show that the equation is bihamiltonian and ...

This paper is concerned with the global existence of dissipative solutions to the Camassa-Holm equation after wave breaking. By introducing a new set of independent and dependent variables, the evolution problem is rewritten as an O.D.E. in an L∞ space, containing a non-local source term which is discontinuous but has bounded directional variation along a suitable cone of directions. For a give...