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arXiv · 2506.19070

From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples

Marianna Euler·Norbert Euler
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Abstract

In this paper we derive two examples of fully-nonlinear symmetry-integrable evolution equations with algebraic nonlinearities, namely one class of 3rd-order equations and a 5th-order equation. To achieve this we study the equations' Lie-Bäcklund symmetries and apply multipotentialisations, hodograph transformations and generalised hodograph transformations to map the equations to known semilinear integrable evolution equations. As a result of this, we also obtain interesting symmetry-integrable quasilinear equations of order five and order seven, which we display explicitly.

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Marianna Euler, Norbert Euler. 2025-07-25. From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples. https://doi.org/10.46298/ocnmp.15938

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