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<p>This paper studies a (2+1)-dimensional fourth-order nonlinear equation from mathematical physics. Using the positive quadratic function method, we explore interactions among lump waves, solitary waves, and periodic waves. We also derive a new type of interaction solution containing a flexible function that can be freely chosen. By testing different forms of this function, we observe and analyze how these waves combine, including mixed behaviors of solitons, periodic patterns, and localized lumps. Finally, we check how stable the solutions are, calculate their wave speeds, and build a D’Alembert-type wave solution using the Ansätze method. This work provides clear examples of complex wave interactions in nonlinear systems.</p>

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(2+1)-Dimensional fourth-order nonlinear equation: interaction solutions and dynamic analysis of waves in mathematical physics

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Li-Juan Peng

摘要

This paper studies a (2+1)-dimensional fourth-order nonlinear equation from mathematical physics. Using the positive quadratic function method, we explore interactions among lump waves, solitary waves, and periodic waves. We also derive a new type of interaction solution containing a flexible function that can be freely chosen. By testing different forms of this function, we observe and analyze how these waves combine, including mixed behaviors of solitons, periodic patterns, and localized lumps. Finally, we check how stable the solutions are, calculate their wave speeds, and build a D’Alembert-type wave solution using the Ansätze method. This work provides clear examples of complex wave interactions in nonlinear systems.