A Synthetical Two‐Component Model with Peakon Solutions

Xia, Bao‐Hui; Zhang, Qiao; Zhou, Ruguang

doi:10.1111/sapm.12085

Cited by 62 publications

(71 citation statements)

References 41 publications

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“…In fact, both system (1.5) with b = 0 and system (6.1) belong to a more general negative flow in a hierarchy. For the details of this topic, one may see our very recent paper [44]. It is an interesting task to study whether there are other new features in the structure of solutions for our two-component system, and particularly for our complex equation with a linear dispersive term.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

A new two-component integrable system with peakon solutions

Xia

Zhang²

2015

Proc. R. Soc. A.

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where b is an arbitrary real constant, is proposed in this paper. This system is shown integrable with its Lax pair, bi-Hamiltonian structure and infinitely many conservation laws. Geometrically, this system describes a non-trivial one-parameter family of pseudo-spherical surfaces. In the case b = 0, the peaked soliton (peakon) and multipeakon solutions to this two-component system are derived. In particular, the two-peakon dynamical system is explicitly solved and their interactions are investigated in details. Moreover, a new integrable cubic nonlinear equation with linear dispersionis obtained by imposing the complex conjugate reduction v = u * to the two-component system. The complex-valued N-peakon solution and kink wave solution to this complex equation are also derived.

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Section: Conclusion and Discussionmentioning

confidence: 99%

A new two-component integrable system with peakon solutions

Xia

Zhang²

2015

Proc. R. Soc. A.

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“…where 2 C , 3 C , 4 C and 5 C denote integration constants. Moreover, with the help of Equation (11), we easily obtain that …”

Section: Two-peakon Solutions To Equation (2)mentioning

confidence: 99%

“…It is a natural idea to continue studying multi-component generalizations of peakon equations. One of the most popular two-component integrable systems, which admits Lax Pair and infinitely conservation laws, has multi-peakon solitons [3]. A three-component model with peakon solutions has been studied by Geng and Xue [4].…”

Section: Introductionmentioning

confidence: 99%

Double-Peakon Solutions of Two Four-Component Camassa-Holm Type Equations

Li¹,

Zha²

2016

JAMP

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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 described in an explicit formula by the method of variation of constant for ordinary differential equations. These double peakon solutions are established in weak sense. The dynamic behaviors of the obtained double peakon solutions are illustrated by some figures.

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“…The equation in (1.2) is completely integrable and can be rewritten as the bi-Hamiltonian form [1], that is…”

Section: Introductionmentioning

confidence: 99%