The Camassa–Holm equation can be written as the system of equations: $${\displaystyle {\begin{aligned}u_{t}+uu_{x}+p_{x}&=0,\\p-p_{xx}&=2\kappa u+u^{2}+{\frac {1}{2}}\left(u_{x}\right)^{2},\end{aligned}}}… In fluid dynamics, the Camassa–Holm equation is the integrable, dimensionless and non-linear partial differential equation The equation was introduced by Roberto Camassa and See more Introducing the momentum m as $${\displaystyle m=u-u_{xx}+\kappa ,\,}$$ then two compatible Hamiltonian descriptions of the Camassa–Holm equation are: See more Traveling waves are solutions of the form $${\displaystyle u(t,x)=f(x-ct)\,}$$ representing waves of permanent shape f that propagate at constant speed c. These waves are called … See more In the spatially periodic case, the Camassa–Holm equation can be given the following geometric interpretation. The group $${\displaystyle \mathrm {Diff} (S^{1})}$$ See more The Camassa–Holm equation is an integrable system. Integrability means that there is a change of variables (action-angle variables) such that the evolution equation in the new variables is equivalent to a linear flow at constant speed. This change of variables … See more The Camassa–Holm equation models breaking waves: a smooth initial profile with sufficient decay at infinity develops into either a wave that exists for all times or into a breaking … See more • Degasperis–Procesi equation • Hunter–Saxton equation See more Web17 Oct 2024 · In this article, we consider the exact solutions to the simplified modified Camassa-Holm (SMCH) equation which has many potential applications in mathematical physics and engineering sciences. We examine the exact travelling wave solutions by means of the modified simple equation (MSE) method by making use of travelling …
Camassa-Holm system - arXiv
Web8 Feb 2024 · In this paper, we consider the rotational Camassa–Holm equation on the circle. Sufficient conditions on the initial data to guarantee wave breaking are established. 1. Introduction Recently, a rotational Camassa–Holm equation was proposed in [ 1 – 4 ], which reads as with where is a parameter related to the Coriolis effect. WebI hold a PhD in Mathematics and I worked as Visiting Researcher at UMASS, MA, USA. I am an experienced Researcher and I have published a lot of scientific papers in high-quality International... cringey pet names
[1509.00694v1] Curvature computations for a two-component Camassa-Holm ...
Webgauge equivalent counterpart of the GHFE is the modified Camassa-Holm equation (mCHE) with an arbitrary parameter κ. Finally, the 1-soliton solution of the GHFE is obtained. 1 Introduction This work continues our research of Lax-integrable (i.e., admitting Lax pairs with non-vanishing spectral parameter) generalized Heisenberg ferromagnet WebWe consider higher-order Camassa–Holm equations describing exponential curves of the manifold of smooth orientation-preserving diffeomorphisms of the unit circle in the plane. … WebCamassa-Holm system on the real line. We obtain the global weak solu-tions via a coordinate transformation into the Lagrangian coordinates. The key ingredients in our analysis are the energy density given by the positive Radon measure and the proposed new distance functions as well. 2010 Mathematics Subject Classification: 35G55, 35B35, … cringey people