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Zero-filter limit issue for the Camassa–Holm equation in Besov spaces
In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of...
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On the isospectral problem of the Camassa–Holm equation
In this paper, we study an isospectral problem of a weighted Sturm–Liouville equation with the Dirichlet boundary condition, which lies at the basis...
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Modulation Analysis of the Stochastic Camassa–Holm Equation with Pure Jump Noise
We study the stochastic Camassa–Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave...
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The Cauchy Problem for the Camassa-Holm-Novikov Equation
In this paper, we consider the Cauchy problem for the Camassa-Holm-Novikov equation. First, we establish the local well-posedness and the blow-up...
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Solutions of the Camassa-Holm Equation Near the Soliton
In this paper, solutions of the Camassa-Holm equation near the soliton Q is decomposed by pseudo-conformal transformation as follows: λ 1/2 ( t ) u ( t, λ ( t )
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Non-uniform Continuity of the Generalized Camassa–Holm Equation in Besov Spaces
In this paper, we consider the Cauchy problem for the generalized Camassa–Holm equation proposed by Hakkaev and Kirchev (Commun Partial Differ Equ...
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Ill-posedness for a generalized Camassa–Holm equation with higher-order nonlinearity in the critical Besov space
In this paper, we prove that the Cauchy problem for a generalized Camassa–Holm equation with higher-order nonlinearity is ill-posed in the critical...
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Orbital stability of periodic peakons for the higher-order modified Camassa–Holm equation
Considered herein is the orbital stability of the periodic peaked solitons for the higher-order modified Camassa–Holm equation. This equation can be...
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On the Integration of the Periodic Camassa–Holm Equation with an Integral-Type Source
AbstractIn the present paper, we study the integration of the periodic Camassa–Holm equation with an integral-type source. Physically, sources arise...
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Persistence properties and blow-up phenomena for a generalized Camassa–Holm equation
In this paper, we investigate a generalized Camassa–Holm equation. Firstly, we establish the persistence properties of strong solutions for the...
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Stability of traveling wave solutions for the second-order Camassa–Holm equation
This paper studies the stability of traveling wave solutions of the second-order Camassa–Holm equation. Applying the pseudo-conformal transformation,...
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The Camassa-Holm approximation to the double dispersion equation for arbitrarily long times
In the present paper we prove the validity of the Camassa-Holm equation as a long wave limit to the double dispersion equation which describes the...
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Orbital Stability of Peakons for the Modified Camassa—Holm Equation
In this paper, we investigate the orbital stability of the peaked solitons (peakons) for the modified Camassa—Holm equation with cubic nonlinearity....
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A Riemann–Hilbert approach to the modified Camassa–Holm equation with step-like boundary conditions
The paper aims at develo** the Riemann–Hilbert (RH) approach for the modified Camassa–Holm (mCH) equation on the line with non-zero boundary...
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Wave-breaking phenomena and Gevrey regularity for the weakly dissipative generalized Camassa–Holm equation
This paper aims to establish a mechanism for the blow-up on a class of weakly dissipative shallow-water equations with a vavariable dipersion term,...
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Existence of the Periodic Peaked Solitary-Wave Solutions to the Camassa–Holm–Kadomtsev–Petviashvili Equation
Considered in this paper is the Camassa–Holm–Kadomtsev–Petviashvili (CH–KP) equation [
22 ], which can be obtained as a model for the propagation of... -
Sharp ill-posedness for the generalized Camassa–Holm equation in Besov spaces
In this paper, we consider the Cauchy problem for the generalized Camassa–Holm equation that containing, as its members, three integrable equations:...
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Stability of periodic peaked solitary waves for a cubic Camassa–Holm-type equation
We investigate the orbital stability of the periodic peaked solitary wave solutions for the cubic Camassa–Holm-type equation which arises as an...
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On the Cauchy problem for a weakly dissipative coupled Camassa–Holm system
This paper is concerned with the local well-posedness, wave breaking, blow-up rate and global existence of solutions for a weakly dissipative coupled...