The Camassa Holm equation: conserved quantities and the initial value problem
نویسندگان
چکیده
منابع مشابه
The Camassa Holm Equation: Conserved Quantities and the Initial Value Problem
Using a Miura-Gardner-Kruskal type construction, we show that the Camassa-Holm equation has an infinite number of local conserved quantities. We explore the implications of these conserved quantities for global well-posedness.
متن کاملExtended Camassa-Holm Hierarchy and Conserved Quantities
An extension of the Camassa-Holm hierarchy is constructed in this letter. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived. PACS: 02.30.Ik; 05.45.Yv; 45.20.Jj; 02.30.Jr.
متن کاملInitial boundary value problem and asymptotic stabilization of the Camassa-Holm equation on an interval
We investigate the nonhomogeneous initial boundary value problem for the Camassa-Holm equation on an interval. We provide a local in time existence theorem and a weak strong uniqueness result. Next we establish a result on the global asymptotic stabilization problem by means of a boundary feedback law.
متن کاملInitial Boundary Value Problem and Asymptotic Stabilization of the Two-Component Camassa-Holm Equation
and Applied Analysis 3 Let T be a positive number. In the following we take ΩT 0, T × 0, 1 . Let vl and vr be in C0 0, T , R and m0 ∈ L∞ 0, 1 , ρ0 ∈ W1,∞ 0, 1 . We set Γl {t ∈ 0, T | vl t > 0}, Γr {t ∈ 0, T | vr t < 0}. 1.3 In the following, we will always suppose that the sets Pl {t ∈ 0, T | vl t 0}, Pr {t ∈ 0, T | vr t 0} 1.4 have a finite number of connected components. Finally, let ml, ρl ∈...
متن کاملRemarks on the Conserved Densities of the Camassa-holm Equation
It is pointed out that the higher-order symmetries of the Camassa-Holm (CH) equation are nonlocal and nonlocality poses problems to obtain higher-order conserved densities for this integrable equation (J. Phys. A: Math. Gen. 2005, 38 869-880). This difficulty is circumvented by defining a nolinear hierarchy for the CH equation and an explicit expression is constructed for the nth-order conserve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physics Letters A
سال: 1999
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(99)00466-1