Higher-Order Pole Solutions of the (2+1) Dimensional Cdgksequation

The present study is devoted to the systematic construction of a novel class of N- multipole solutions for the (2+1) dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) e- quation. Within the inverse scattering transform formalism, we address the technically demanding regime where the underlying transmission coefficient exhibits multiple pairs of higher-order singulari- ties. The formulation of the inverse problem as a 2×2 matrix Riemann-Hilbert problem, supplemented by discrete residue constraints, reveals that potential reconstruction in the reflectionless case collapses into a closed-form linear algebraic system. Drawing upon the algebraic properties of generalized con- fluent Cauchy matrices, Gram matrices, and Jordan-associated polynomial functions, we rigorously establish the well-posedness of the solution for all (x,y,t) ∈ R2× R+. This foundation allows for the derivation of compatible higher-order pole solutions within the mKdV and fifth-order mKdV equation- s. Subsequently, explicit multipole solutions for the (2+1) dimensional CDGKS equation are obtained by invoking integrable decomposition and modular square transformations. Numerical visualizations further elucidate the dynamical evolution and density profiles of these localized waves, revealing the intricate interaction patterns of higher-order, bound-state solitons and breathers.