Two new Wronskian conditions for the (3 + 1)-dimensional Jimbo–Miwa equation

New Wronskian Representation of Solution for a Variable-Coefficient Kadomtsev—Petviashvili Equation

“…( 1). The new Wronskian condition is a system of combined equations and differs from the previous Wronskian conditions ( 6) and (7). The particular forms of Wronskian determinant solutions include 𝑁 -soliton solutions, trigonometric function solutions and rational solutions.…”

“…The most important procedure of the Wronskian technique is to choose the so-called Wronskian conditions that the generating functions in the Wronskian determinant satisfy. [5,7] The main tool to establish the Wronskian representations is the Plücker relation for determinants. [11,12] In this Letter, we give a new Wronskian representation of solution to the variable-coefficient Kadomtsev-Petviashvili (vcKP) equation [13−15] [𝑢 𝑡 + 𝑓 (𝑡)𝑢𝑢 𝑥 + 𝑔(𝑡)𝑢 𝑥𝑥𝑥 ] 𝑥 + ℎ(𝑡)𝑢 𝑦𝑦 = 0, (1) under the constraint 𝑓 (𝑡) = 6 𝐶0 𝑔(𝑡).…”

“…( 1) by utilizing the Wronskian technique. For this purpose, we still consider the 𝑁 th order Wronskian determinant (5), with, however, the generating functions 𝜑 𝑖 (1 ≤ 𝑖 ≤ 𝑁 ) in the Wronskian determinant satisfying different differential equations compared with the previous Wronskian conditions ( 6) and (7). A theorem is given as follows.…”