Abstract We revisit the Fermi–Pasta–Ulam–Tsingou lattice (FPUT) with quadratic and cubic
nonlinear interactions in the continuous limit by deducing the Gardner equation. Through the …

Higher order mKdV breathers: nonlinear stability ∗ Page 1 Higher order mKdV breathers:
nonlinear stability ∗ Miguel A. Alejo Universidad de Córdoba, Spain Received : April 2023 …

In this paper, numerical solution of both the combined KdV and modified KdV equation (KdV-
MKdV) known as Gardner equation and Harry Dym equation are obtained using quartic B …

Abstract The Kaup–Newell (KN) hierarchy contains the derivative nonlinear Schrödinger
equation (DNLSE) amongst others interesting and important nonlinear integrable equations …

Abstract The construction of Integrable Hierarchies in terms of zero curvature representation
provides a systematic construction for a series of integrable non-linear evolution equations …

We present a new variational characterization of breather solutions of any equation of the
focusing Gardner hierarchy. This hierarchy is characterized by a nonnegative index n, and …

We propose an approach to the nonvanishing boundary value problem for integrable
hierarchies based on the dressing method. Then we apply the method to the AKNS …

In this work, we deal with the initial value problem of the 5th-order Gardner equation in R,
presenting the local well-posedness result in H 2 (R). As a consequence of the local result …

Integrable mixed models have been used as a generalization of traditional integrable
models. However, a map from a traditional integrable model to a mixed integrable model is …

We are interested in stability results for breather solutions of the 5th, 7th and 9th order mKdV
equations. We show that these higher order mKdV breathers are stable in $ H^ 2 (\R) $, in …