We aim, in this paper, to present a formal interacting string solution for the MigdalMakeenko Loop Wave Equation for the colour group (U(Nc)) (Ref. [1] and references therein). Our main tool to solve the Migdal-Makeenko Loop Wave Equation is based on the remark made in the Section 1 of this note, where we address the problem of solving critical string wave equations by string functional integra...

In this paper, we consider variform exact peakon solutions for four nonlinear wave equations. We show that under different parameter conditions, one nonlinear wave equation can have different exact one-peakon solutions and different nonlinear wave equations can have different explicit exact one-peakon solutions. Namely, there are various explicit exact one-peakon solutions, which are different ...

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlevé property. We then solve the LSRI equation using Painlevé truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide ...

To study the spiral wave in an unbounded excitable medium, we consider the wave front interaction model which derived by Zykov in 2007. This model consists of two systems of ordinary di↵erential equations which describe the wave front and wave back, respectively. First, we derive some properties of the back by shooting argument and comparison principle. Next we show the global existence of the ...

We study the asymptotic stability of a plane CJ detonation wave under the assumption of small resolved heat release (SRHR). We prove that the solution exists globally and that the solution converges uniformly to a shifted CJ detonation wave as t! + 1 for initial data which are small perturbations of the CJ detonation wave. The weighted energy method is used to overcome the diiculty arising from...

The inflow problem of full compressible Navier-Stokes equations is considered on the half line (0,+∞). Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state (ρ+, u+, θ+) belongs to the subsonic, transonic and supersonic regions respectively. Then the asymptotic stability of not only the single contact wave but also the su...

In this paper, the modified exp-function method is used to seek generalized wave solutions of Klein-Gordon equation. As a result, some new types of exact traveling wave solutions are obtained which include kink wave solutions, periodic wave solution, and solitary wave solutions. Obtained results clearly indicate the reliability and efficiency of the proposed modified exp-function method.