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## Rational solitons in the Gardner-like models

Rational solutions of nonlinear evolution equations are considered in the literature as a

mathematical image of rogue waves, which are anomalously large waves that occur for a short time.

In this work, bounded rational solutions of Gardner-type equations (the extended Korteweg-de

Vries equation), when a nonlinear term can be represented as a sum of several terms with arbitrary

powers (not necessarily integer ones), are found. It is shown that such solutions describe first-order

algebraic solitons, kinks, and pyramidal and table-top solitons. Analytical solutions are obtained for

the Gardner equation with two nonlinear terms, the powers of which differ by a factor of 2. In other

cases, the solutions are obtained numerically. Gardner-type equations occur in the description of

nonlinear wave dynamics in a fluid layer with continuous or multilayer stratification, as well as in

multicomponent plasma, and their solutions are used for the interpretation of rogue waves.