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<p>The paper studies soliton solutions of the coupled Schrödinger–Boussinesq equation, which describes two short waves and a long wave in nonlinear dispersive media. The one-, two-, three- and <i>N</i>-soliton solutions are obtained using the Hirota bilinear method. As the primary step, we achieve breather-like solutions that exhibit similar breather behaviours. Through systematic variation of the parameters in the power series expansions, we derive single-hump bright and dark soliton solutions. Double-hump bright solitons are constructed after changing the power series expansion forms of <i>g</i> and <i>h</i>. Furthermore, we utilise asymptotic analysis to examine the interaction properties of single-hump and double-hump two-bright solitons. Ultimately, graphical simulation better demonstrates dynamics behaviours of solitons.</p>

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Multi-soliton solutions and dynamic behaviours in coupled Schrödinger–Boussinesq equation

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Zeting Li,
  • Ben Gao

摘要

The paper studies soliton solutions of the coupled Schrödinger–Boussinesq equation, which describes two short waves and a long wave in nonlinear dispersive media. The one-, two-, three- and N-soliton solutions are obtained using the Hirota bilinear method. As the primary step, we achieve breather-like solutions that exhibit similar breather behaviours. Through systematic variation of the parameters in the power series expansions, we derive single-hump bright and dark soliton solutions. Double-hump bright solitons are constructed after changing the power series expansion forms of g and h. Furthermore, we utilise asymptotic analysis to examine the interaction properties of single-hump and double-hump two-bright solitons. Ultimately, graphical simulation better demonstrates dynamics behaviours of solitons.