Wronskian solutions, Grammian solutions and lump molecules for a (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation

Zhimin Ma; Zhimin Ma

doi:10.3934/math.2026505

AIMS Mathematics

2026, Volume 11, Issue 4: 12323-12333. doi: 10.3934/math.2026505

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Research article

Wronskian solutions, Grammian solutions and lump molecules for a (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation

Zhimin Ma ^,

The Engineering and Technical College of Chengdu University of Technology, Leshan 614000, China

Received: 06 March 2026 Revised: 12 April 2026 Accepted: 24 April 2026 Published: 30 April 2026
MSC : 35Q51, 37K35

This paper investigates the exact solutions and dynamical properties of the (2+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation. First, using the bilinear method and complex linear systems, we theoretically prove that the equation admits Wronskian and Grammian determinant solutions, establishing the mathematical completeness of its solution structure. Second, based on the Grammian determinant solutions, we thoroughly analyze the complex localized wave behaviors exhibited by lump solutions during anomalous scattering. The results reveal that the system supports a novel bound state, lump molecules, i.e., stable composite structures formed by nonlinear interactions among multiple lump solutions, which subsequently propagate coherently. These findings not only uncover rich dynamical phenomena inherent to the YTSF equation, but also provide new theoretical insights into the formation and evolution mechanisms of multi-lump bound states in nonlinear partial differential equations.
- Wronskian solutions,
- Grammian solutions,
- lump molecules
Citation: Zhimin Ma. Wronskian solutions, Grammian solutions and lump molecules for a (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation[J]. AIMS Mathematics, 2026, 11(4): 12323-12333. doi: 10.3934/math.2026505

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Abstract

This paper investigates the exact solutions and dynamical properties of the (2+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation. First, using the bilinear method and complex linear systems, we theoretically prove that the equation admits Wronskian and Grammian determinant solutions, establishing the mathematical completeness of its solution structure. Second, based on the Grammian determinant solutions, we thoroughly analyze the complex localized wave behaviors exhibited by lump solutions during anomalous scattering. The results reveal that the system supports a novel bound state, lump molecules, i.e., stable composite structures formed by nonlinear interactions among multiple lump solutions, which subsequently propagate coherently. These findings not only uncover rich dynamical phenomena inherent to the YTSF equation, but also provide new theoretical insights into the formation and evolution mechanisms of multi-lump bound states in nonlinear partial differential equations.

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