Non-Classical Traveling Solutions in a Nonlinear Klein Gordon Model

Abstract

A model with interparticle inharmonic interaction under the 4 external potential is studied. Making use of the special relation of relevant parameters, in the continuous limit, it was possible to obtain various non-classical soliton solutions, specifically, compact and peak-like solutions. The solutions undergo a jump on their first derivatives at some points of the space-time manifold. These analytic solutions were obtained by considering strong restrictions on their velocities and on the jump conditions. The energy concentrated in these solutions shows in several cases a discrete spectrum.

Traveling wave solutions of the nonlinear dispersive Klein–Gordon equations

“…The dimensionless form of the nonlinear dispersive KGE that is going to be studied in this paper is given by (Aguero et al, 2009) …”

“…Klein-Gordon equation (KGE) appears in the study of relativistic Quantum Mechanics (Aguero et al, 2009;Basak et al, 2009;Bawin and Jaminon, 1984;Biswas et al, 2008;Chen, 2005;Cheng, 2011;Comay, 2004;Lakshmi, 2009;Li et al, 2010;Sassaman and Biswas, 2009, 2010a,b, 2011Yasuk et al, 2006;Zheng and Lai, 2009). There are various studies on this equation that has been conducted during the past decades.…”

“…The nonlinear dispersive KGE appeared in 2009 (Aguero et al, 2009). In this paper, this nonlinear dispersive KGE will be studied by the aid of traveling wave hypothesis.…”

Compacton-Like Solutions in a Camassa–Holm Type Equation

“…Recently, some researchers obtained many kinds of compacton-like solutions, compacton-like kinks in the generalized φ-four or double-well model with nonlinear coupling, [8] double compacton-like solutions in the Olver-Rosenau equation [9] and anti-bubble compacton in the nonlinear Klein Gordon model. [10] Furthermore, the possibility of these compact solutions arising from the nonlinear equations, relevant for physical problems, will make them amenable for experimental detection.…”

Exact traveling wave solutions of the perturbed Klein-Gordon equation with quadratic nonlinearity in (1+1)-dimension, Part I-without local inductance and dissipation effect

“…Applying the trigonometric function series method, Zhang [2] In the absence of perturbed terms, there is a large literature concerning the exact traveling wave solutions of the KGE and generalized Klein-Gordon equation (gKGE), as we can see in [28][29][30][31][32][33]. In [30], Sassaman and Biswas obtained the exact 1-soliton solution of 5 different forms of the gKGE by using the solitary wave solution ansatz.…”