Abstract
With the help of the direct bilinear method, explicit rational and rational–exponential solutions to a dimensionally reduced generalized Jimbo–Miwa equation are derived by assuming the auxiliary function as the quadratic function and the combinations of the quadratic function and the exponential one. It is shown that three kinds of exact solutions describe the lump, the interaction consisting of one lump and one stripe soliton, and the rogue wave arising from the stripe soliton pair respectively. Local characteristics and interaction properties for these mixed nonlinear waves are analyzed in detail.
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