Titlebook: Nonlinear Systems, Vol. 1; Mathematical Theory Victoriano Carmona,Jesús Cuevas-Maraver,Elisabeth Book 2018 Springer Nature Switzerland AG

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Normal Form for a Class of Three-Dimensional Systems with Free-Divergence Principal Part the principal part of the vector field. We focus on a class of tridimensional systems whose principal part is the coupling of a Hamiltonian planar system and an unidimensional system, in such a way that the quoted principal part does not depend on the last variable and has free divergence. Our stud

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Piecewise-Linear (PWL) Canard Dynamics . (one slow and one fast variables) and . (two slow and one fast variables), we prove the existence of (maximal) canard solutions and show that the main salient features from smooth systems is preserved. We also highlight how the PWL setup carries a level of simplification of singular perturbation

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Solitary Waves in the Nonlinear Dirac Equation Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subseque

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Adiabatic Invariants of Second Order Korteweg-de Vries Type Equationer equations for shallow water are extended to the second order, beyond Korteweg-de Vries (KdV). We show that contrary to KdV for which there is an infinite number of invariants, for KdV2 there exists only one, connected to mass (volume) conservation of the fluid. For KdV2 we found only so-called .,

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A Logistic Non-linear Difference Equation with Two Delaysations with respect to seasons in time .. Of special interest are those non-linear equations with two delays, particularly due to the effect of food in the evolution of the population. As an adequate tool to understand the behaviors of solutions of the equation, we use an unfolding of it obtaining a

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