[PDF] Top 20 Multisymplectic method for the Camassa Holm equation

... this equation: Degasperis et ...Degasperis-Procesi equation is also integrable and admits multipeakon ...Degasperis-Procesi equation and proved that the schemes converge to entropy ...b-family ... See full document

... tanh method [2] [3], the Jacobi elliptic function expansion [4]-[14], differential quadrature method [15], the truncated Painleve expansion [16], Lie classical method [17], Hirota bilinear ... See full document

... solution method is similar to the one that we have used previously to find periodic and solitary travelling-wave solutions to the Degasperis–Procesi equation [4], the Camassa–Holm ... See full document

... elliptic method [6], the standard tanh and extended tanh methods [7-11], the exp-function method [12-13], the inverse scattering method [14] and others have been proposed to obtain exact solutions of ... See full document

... general method of tri-Hamiltonian duality to the bi-Hamiltonian rep- resentation of the modified Korteweg-de Vries ...that equation (.) is related to the short-pulse equation derived by Schäfer and ... See full document

... perturbation method (VHPM) has been studied to obtain soli- tary wave solutions of modified Camassa-Holm and Degasperis-Procesi ...above equation compared with VIM, HPM, and exact ...present ... See full document

... Direct Method in Soliton Theory, Cambridge University Press, Cambridge, ...generalized Camassa-Holm equation, ...kdv equation, ... See full document

... dissipative Camassa-Holm equation and k = : the weakly dissipative Novikov ...the method developed by Liu and Yin [] to deal with the Degasperis-Procesi equation ... See full document

... Motivated by the work in [, , , , ], we study the global stabilization of problem (.). Our main results are the existence and uniqueness of global strong solutions, global weak solutions and the exponential ... See full document

... This paper is contributed to study two new integrable four-component systems reduced from a multi-component generation of Camassa-Holm equation. Some double peakon solutions of both systems are ... See full document

... CH equation describes shallow water waves, where u denotes the velocity, x and t denote the spatial and temporal variables, respectively, and k is related to the critical shallow-water wave-speed ...CH ... See full document

... generalized Camassa-Holm equation (gCH) with cubic ...gCH equation are orbitally stable by using the method of Constantin and ...classical Camassa-Holm type ... See full document

... variation method 6. This is in sharp contrast to the Korteweg-de Vries equation, where solitary waves are generally ...the Camassa- Holm equation replicate a future that is ... See full document

... (1.1), Holm [4] not only studied the effects of balance parameter a and kernel function of solitary wave structures but also investi- gated their interactions analytically with ε = 0 and numerically with small ... See full document

... generalized Camassa-Holm equation. It is shown that the equation is locally well posed when the initial data are sufficiently ...generalized Camassa-Holm equation by the ... See full document

... the method of asymptotic density of the momentum to show that under the assumption of its uniqueness, at the momentum level, the solution approaches a train of peakons moving right with different ...Euler ... See full document

... which is a crucial ingredient to obtain the blow-up phenomenon. Last, by using the conserves from laws and the contraction mapping theorem, we obtain the existence of weak solutions of Cauchy problem (1.2) and (1.3). ... See full document

... Taking k = 1, λ = 0, a = 1, b = 2 in (1.1) gives rise to the Cauchy problem of Eq. (1.3). The solution v to Eq. (1.2) is viewed as a perturbation near β (see [20]). The properties of solutions to the problem with ... See full document

... which has been investigated by many scholars. Grayshan [] studied both the periodic and the non-periodic Cauchy problem for Eq. () and discussed continuity results for the data-to-solution map in the Sobolev spaces. A ... See full document

... As we know, differently from the Camassa-Holm equation, Eq. () has not blow-up so- lution. The motivation of the present paper is to find out whether or not system () has some similar dynamics as the ... See full document