The Modified Camassa–Holm Equation
Przemysław Górka , Enrique G. Reyes
AbstractThe Camassa–Holm (CH) equation describes pseudo-spherical surfaces and therefore its integrability properties can be studied by geometrical means [Reyes, “Geometric integrability of the Camassa–Holm equation.” Letters in Mathematical Physics 59 (2002): 117–31]. Using this fact, we introduce a “Miura transform” and a “modified” Camassa–Holm (mCH) equation, in analogy with the Korteweg–de Vries theory. We obtain an infinite number of local conservation laws for CH from these data and also an infinite number of (non)local symmetries. We then compute conservation laws for mCH and also show that it describes pseudo-spherical surfaces, so that, in particular, it is the integrability condition of an -valued linear problem. Finally, we investigate mCH analytically: we define weak solutions and prove their existence and uniqueness.
|Journal series||International Mathematics Research Notices, ISSN 1073-7928, (A 30 pkt)|
|Publication size in sheets||1.6|
|Publication indicators||= 17; = 19; : 2011 = 1.373; : 2011 = 1.014 (2) - 2011=1.087 (5)|
|Citation count*||12 (2014-02-15)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.