Abstract
The multiple rogue wave solutions method is employed for searching the multiple soliton solutions for the new variable-coefficient Kadomtsev–Petviashvili equation, which contains first-order, second-order, third-order, and fourth-order wave solutions. At the critical point, the second-order derivative and Hessian matrix for only one point will be investigated and the lump solution has one maximum value. The physical phenomena of these gained multiple soliton solutions are analysed and indicated in figures by selecting suitable values.
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