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中国物理学会期刊

(2+1)维广义Caudrey–Dodd–Gibbon–Kotera–Sawada方程的团块链与混合相互作用解

Lump chain and hybrid interaction solutions for a (2+1)-dimensional generalized Caudrey–Dodd– Gibbon–Kotera–Sawada equation in fluid dynamics

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  • 本文研究了(2+1)维广义Caudrey–Dodd–Gibbon–Kotera–Sawada方程的团块结构和束缚态分子结构解. 基于孤子解中推导出团块链解,在参数无限趋于零时逐渐退化为具有相同速度的团块解. 两条团块链在退化过程中逐渐形成三个相互作用的团块,并最终演变为共振三角形结构,揭示了状态转换过程中解结构的变化. 此外,在共振条件和参数约束下,从双曲型N孤子解出发,在不同参数调控下推导得到了混合束缚态分子解,如单呼吸-单孤子分子、单呼吸-双孤子分子以及单呼吸-单孤子分子与双孤子分子相互作用. 通过图示可观察到分子之间的弹性碰撞.

     

    The (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada (gCDGKS) equation is an important integrable equation in fluid mechanics. In this paper, a novel type of interacting lump structures and various boundstate molecular solutions for this equation are investigated. The general multi-soliton solutions in hyperbolic function form are constructed via the Hirota bilinear method. Purely imaginary parameters with a key small parameter ε are introduced into the soliton solutions to obtain lump chains. When ε goes to zero, the asymptotic behavior of the lump chains are analyzed. It is found that during the degeneration process, two originally independently propagating lump chains gradually evolve into three lumps with identical velocities, which are closely arranged in space to form a resonant triangular structure. This process clearly reveals the dynamical transition mechanism of lump interactions from the crossing-through interaction with unchanged shapes to the interaction characterized by merging, deformation and resonance. Furthermore, based on the hyperbolic N-soliton solutions, a variety of mixed molecular structures solutions, including one-breather-one-soliton molecule, one-breather-two-soliton molecule and interaction between one-breatherone-soliton molecule and two-soliton molecule are constructed under velocity resonance conditions. The adjustment of the parameters α and β can change the shape of the breather component within the molecules without altering their overall spatial positions. The collision processes among these molecules demonstrate that the interactions between these mixed bound states are always elastic, which verifies the stability of such molecular structure as particle-like excitations. In summary, this work reveals the transition path from interacting lump chains to resonant triangular lump structures and form solitons to various mixed molecular bound states within the (2+1)-dimensional gCDGKS framework.

     

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