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

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.