Higher order solitary solutions to the meta-model of diffusively coupled Lotka–Volterra systems

A meta-model of diffusively coupled Lotka–Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order n is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order $n>3$ n > 3 . Analytical and computational experiments are used to illustrate the obtained results.

Difference equation vs differential equation on different scales

Purpose The purpose of this paper is to demonstrate that the numerical method is not everything for nonlinear equations. Some properties cannot be revealed numerically; an example is used to elucidate the fact. Design/methodology/approach A variational principle is established for the generalized KdV – Burgers equation by the semi-inverse method, and the equation is solved analytically by the exp-function method, and some exact solutions are obtained, including blowup solutions and discontinuous solutions. The solution morphologies are studied by illustrations using different scales. Findings Solitary solution is the basic property of nonlinear wave equations. This paper finds some new properties of the KdV–Burgers equation, which have not been reported in open literature and cannot be effectively elucidated by numerical methods. When the solitary solution or the blowup solution is observed on a much small scale, their discontinuous property is first found. Originality/value The variational principle can explain the blowup and discontinuous properties of a nonlinear wave equation, and the exp-function method is a good candidate to reveal the solution properties.

A note on soliton solutions of Klein-Gordon-Zakharov equation by variational approach

In this paper, an investigation has been made to validate the variational approach to obtain soliton solutions of the Klein-Gordon-Zakharov (KGZ) equations. It is evident that to resolve the non-linear partial differential equations are quite complex and difficult. The presented approach is capable of achieving the condition for continuation of the solitary solution of KGZ equation as well as the initial solutions selected in soliton form including various unknown parameters can be resolute in the solution course of action. The procedure of attaining the solution reveals that the scheme is simple and straightforward.