Web‐Structured Soliton Solutions for the (2+1)‐Dimensional B‐Type Kadomtsev‐Petviashvili Equation

ABSTRACT We investigate the web‐structured soliton solutions of ‐dimensional B‐type Kadomtsev‐Petviashvili (B‐type KP) equation. We initially provided a concise proof that the ‐function of the B‐type KP equation admits a solution in the form of the Wronskian determinant. As is well known, each ‐function corresponds to a specific point on a completely non‐negative Grassmannian manifold . This correspondence facilitates the derivation of web‐structured soliton solutions for the equation. Moreover, the asymptotic behavior of each line soliton in the ‐function can be visually represented and illustrated graphically. We further demonstrate that such solutions have asymptotic line solitons as , which are represented by index pair , while in the opposite direction there are asymptotic line solitons, represented by index pair . We conducted an exhaustive and in‐depth analysis of the asymptotic line solitons within the web‐structured soliton solutions through several examples. Moreover, we explained in detail each asymptotic line soliton contained in the ‐soliton solution by using the rank of certain minors of the matrix .