Solitonic structures in a nonlinear model with interparticle anharmonic interaction

Behavior of gap solitons in anharmonic lattices

Using the theory of bifurcation, we provide and find gap soliton dynamics in a nonlinear Klein-Gordon model with anharmonic, cubic, and quartic interactions immersed in a parametrized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Nonconvex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive a variety of exotic solutions corresponding to the phase trajectories under different parameter conditions. Moreover, we demonstrate how and why traveling waves lose their smoothness and develop into solutions with compact support or breaking.

Generalized Klein-Gordon models: behavior around the ground state condensate

In this work, we investigate the balance between the nonlinear and linear interaction energy of an interparticle anharmonic system in the vicinity of the ground state condensate. As a result, we find that the nonlinear interaction energy is very significant in the vicinity of each degree of freedom. We address some potential applications of the findings to miscellaneous areas of interests such as soliton theory, hydrodynamics, solid state physics, ferromagnetic and ferroelectric domain walls, condensed matter physics, and particle physics, among others.

Painlevé-integrability of a (2+1)-dimensional reaction-diffusion equation: exact solutions and their interactions

We investigate the singularity structure analysis of a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion (NLERD) equation by means of the Painlevé (P) test. Following the Weiss et al.'s formalism [J. Math. Phys. 24, 522 (1983)], we prove the arbitrariness of the expansion coefficients of the observables. Thus, without the use of the Kruskal's simplification, we obtain a Bäcklund transformation of the coupled NLERD equation via a consistent truncation procedure stemming from the Weiss 's methodology [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984)]. In the wake of such results, we unveil a typical spectrum of localized and periodic coherent patterns. We also investigate the scattering properties of such structures and we unearth two peculiar soliton phenomena, namely, the fusion and the fission.