Generalized Wronskian solutions for the (3+1)-dimensional Jimbo–Miwa equation

Rational solutions to a KdV-like equation

“…Their rational solutions, both singular and non-singular, or even rogue wave solutions will be a very interesting topic. Particularly, higher-order rogue wave solutions should be connected with generalized Wronskian solutions [19,20] and generalized Darboux transformations [21,22]. …”

A Wronskian formulation of the (3 + 1)-dimensional generalized BKP equation

“…where Row(B, i) and Col(B, j) denote the ith row and the jth column of B, respectively. Taking B as ( N − 1) and ( N − 2, N ) in equality (15) and then using the condition (7) leads to the above two equalities ( 13) and ( 14). This completes the proof of lemma 2.…”

“…In recent years, more higher-dimensional NLEEs have been investigated, because higher-dimensional NLEEs could have a richer diversity of exact solutions. Many higher-dimensional equations have been proven to possess the Wronskian solutions, such as the (2 + 1)-dimensional breaking soliton equation [10], the (2 + 1)-dimensional soliton equation [11], the (3 + 1)-dimensional KP equation [12] and the (3 + 1)-dimensional Jimbo-Miwa equation [13][14][15]. Very recently, Wronskian and Grammian formulations have been established to the (3 + 1)-dimensional generalized KP equation by Ma et al [16], based on the Plücker relation and the Jacobi identity for determinants.…”

Exact solutions of the (3+1)-dimensional Jimbo-Miwa equation via Wronskian solutions: Soliton, breather, and multiple lump solutions

“…In soliton theory, exact solutions of the nonlinear partial differential equations are widely applied in fluid dynamics, nonlinear optics, plasma physics, and so on [1][2][3][4][5]. There are many different types of exact solutions, such as soliton solutions, periodic solutions, Wronskian solutions, lump solutions and hybrid solutions [6][7][8][9][10].…”