Camassa–Holm equation
Multisymplectic method for the Camassa Holm equation
... The multisymplectic integrator algorithm has aroused considerable interest since it was presented in []. As a very robust framework, this algorithm has many advantages in the process of dealing with some ...
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Existence and nonexistence of solutions for the generalized Camassa Holm equation
... DGH equation via the semigroup approach of quasi- linear hyperbolic equations of evolution and the viscosity ...the Camassa-Holm ...Dullin-Gottwald-Holm equation and derived a sufficient ...
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The global stabilization of the Camassa-Holm equation with a distributed feedback control
... 6. Yin, ZY: On the Cauchy problem for an integrable equation with peakon solutions. Ill. J. Math. 47, 649-666 (2003) 7. Constantin, A: On the scattering problem for the Camassa-Holm equation. ...
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Exact Traveling Wave Solutions for Generalized Camassa Holm Equation by Polynomial Expansion Methods
... generalized Camassa-Holm ...generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function ...
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Blow up for the weakly dissipative generalized Camassa Holm equation
... Remark . The result in Theorem . contains the cases for k = : the weakly dissipative Camassa-Holm equation and k = : the weakly dissipative Novikov equation. We used the method developed ...
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Random attractor for a stochastic viscous coupled Camassa Holm equation
... The paper is organized as follows. In the next section, we review the pullback random attractor theory for random dynamical systems and some lemmas. In Section , we define a random dynamical system for the stochastic ...
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An asymptotic property of the Camassa-Holm equation on the half-line
... the Camassa-Holm equation on the half ...the Camassa-Holm equation with initial data u ∈ H s (R + ) ∩ H (R + ), s > , where R + = [, ...
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The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
... the Camassa-Holm equation and other partial differential equations, the reader is referred to ...wave equation (or a generalized Camassa-Holm equation), namely, λ = , β = ...
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Attractor for a Viscous Coupled Camassa Holm Equation
... Vries equation, where solitary waves are generally ...the Camassa- Holm equation replicate a future that is characteristic for waves of great height–waves of the largest amplitude that are ...
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Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method
... The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa–Holm equation. This approximate solution, which is ob- tained as a series of exponentials, ...
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Orbital Stability of Peakons for a Generalized Camassa Holm Equation
... generalized Camassa-Holm equation (gCH) with cubic ...gCH equation are orbitally stable by using the method of Constantin and ...classical Camassa-Holm type equation ...
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Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method
... G = G η satisfies G '' + λ G ' + µ G = 0 and obtained some exact traveling wave solutions in terms of hyperbolic, periodic and rational functions. Another authors, Liu et al. [28] applied the basic ( G G '/ ) - expansion ...
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Local well-posedness and persistence properties for a model containing both Camassa-Holm and Novikov equation
... The Camassa-Holm equation ...the Camassa-Holm spectral problem yields two different integrable hierarchies of nonlinear evolution equations, one is of negative or- der CH hierachy while ...
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Double Peakon Solutions of Two Four Component Camassa Holm Type Equations
... 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 ...
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Global weak solutions for a generalized Dullin-Gottwald-Holm equation in the space H1(R)
... DGH equation was also discussed in [] and it was established that, similarly to the Camassa-Holm equation, singularities can arise only in the form of wave breaking, namely, the solution ...
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Wave breaking and infinite propagation speed for a modified two component Camassa Holm system with κ≠0
... the Camassa-Holm equation, which was derived physically by Camassa and Holm in [] (found earlier by Fokas and Fuchssteniner [] as a bi-Hamiltonian generalization of the KdV ...
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A wave breaking criterion for a modified periodic two component Camassa Holm system
... 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 ...
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The optimal control problem with necessity condition for a viscous shallow water equation
... (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 ...
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Persistence properties for the Fokas-Olver-Rosenau-Qiao equation in weighted \(L^{p}\) spaces
... the Camassa-Holm equation in comparison with the KdV equation lies in the fact that the Camassa-Holm equation has peaked soli- tons and models peculiar wave breaking ...
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Some periodic and solitary travelling-wave solutions of the short pulse equation
... The aim of the present paper is to complement the work in [3] by presenting other travelling-wave solutions to the SPE. The solution method is similar to the one that we have used previously to find periodic and solitary ...
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