Scholarlink

<p>Perturbative expansion and soliton solutions of the (3+1)-dimensional Boussinesq equation are studied in the present paper. Through a perturbative expansion method, the (3+1)-dimensional nonlinear Schrödinger equation is derived. Additionally, by employing a Galilean transformation, a (3+1)-dimensional-like Korteweg–de Vries (KdV) equation is also obtained, offering a novel perspective for exploring the physical properties of the Boussinesq equation. Focusing on the soliton solutions of the equation, the modified CK (m-CK) method is employed to establish relationships between new and existing solutions, and the Hirota bilinear method to derive multi-soliton solutions, thereby enriching the solution space. These findings reveal that the new solutions exhibit improved stability and weaker interactions compared to the existing ones, highlighting their potential for practical applications.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Perturbative expansion and new soliton solutions of the (3+1)-dimensional Boussinesq equation in fluid mechanics

  • 期刊论文

  • 发表日期：

    2026年6月20日

查看全文
  • Gangwei Wang,
  • Zixuan Tan,
  • Abdul-Majid Wazwaz,
  • Zhuoheng Li

摘要

Perturbative expansion and soliton solutions of the (3+1)-dimensional Boussinesq equation are studied in the present paper. Through a perturbative expansion method, the (3+1)-dimensional nonlinear Schrödinger equation is derived. Additionally, by employing a Galilean transformation, a (3+1)-dimensional-like Korteweg–de Vries (KdV) equation is also obtained, offering a novel perspective for exploring the physical properties of the Boussinesq equation. Focusing on the soliton solutions of the equation, the modified CK (m-CK) method is employed to establish relationships between new and existing solutions, and the Hirota bilinear method to derive multi-soliton solutions, thereby enriching the solution space. These findings reveal that the new solutions exhibit improved stability and weaker interactions compared to the existing ones, highlighting their potential for practical applications.