Multiple higher-order pole solutions for matrix-type Lakshmanan-Porsezian-Daniel equation

Abstract In this paper, we employ the inverse scattering transform to analyze the matrix-type Lakshmanan-Porsezian-Daniel equation under the zero boundary conditions. The analysis focuses on multiple higher-order poles that are associated with different transmission coefficients. For the direct and inverse problems of the inverse scattering transform, the generalized cross product in four-dimensional space is introduced with the aim of facilitating a more detailed analysis of these properties. Subsequently, the Riemann-Hilbert approach is used to derive the reconstruction formula. Under the condition of reflectionless potential, the multiple higher-order pole solutions of the equation are obtained, and the properties of the solutions are graphically displayed.