Related papers: QCD traveling waves beyond leading logarithms
This paper presents results on the unboundedness and minimal speed of traveling wave solutions for a one-dimensional spatial reaction-diffusion equation with an asymptotically linear reaction term and a saturation parameter. By applying a…
We consider the semi linear Fisher-Kolmogorov-Petrovski-Piscounov equation for the advance of an advantageous gene in biology. Its non-smooth reaction function $f(u)$ allows for the introduction of travelling waves with a new profile. We…
For both cubic and quintic nonlinearities of the one-dimensional complex Ginzburg-Landau evolution equation, we prove by a theorem of Eremenko the finiteness of the number of traveling waves whose squared modulus has only poles in the…
This paper reports results on the classification of traveling wave solutions, including nonnegative weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches…
We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are…
We construct non-localized, real global solutions of the Kadomtsev-Petviashvili-I equation which vanish for $x\to-\infty$ and study their large time asymptotic behavior. We prove that such solutions eject (for $t\to\infty$) a train of…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…
Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken $x_{\rm B}$, as they are supposed to restore an upper bound of unitarity for the cross section of high energy scattering. In…
This article concludes the study of (2+1)-dimensional nonlinear wave equations that can be derived in a model of an ideal fluid with irrotational motion. In the considered case of identical scaling of the $x,y$ variables, obtaining a…
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force…
The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of…
We study the existence, regularity, and symmetry of periodic traveling solutions to a class of Gardner-Ostrovsky type equations, including the classical Gardner-Ostrovsky equation, the (modified) Ostrovsky, and the reduced (modified)…
When computed to next-to-leading order in perturbative QCD, the non-linear Balitsky-Kovchegov (BK) equation for the high-energy evolution of the dipole-hadron scattering appears to be unstable. We show that this instability can be avoided…
We identify the nonlinear evolution equation in impact-parameter space for the "Supercritical Pomeron" in Reggeon Field Theory as a 2-dimensional stochastic Fisher and Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity…
We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there is a branch of traveling waves solutions with nonvanishing…
We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…
We give a detailed study of the traveling wave solutions of $(\ell=2)$ Kaup-Boussinesq type of coupled KdV equations. Depending upon the zeros of a fourth degree polynomial, we have cases where there exist no nontrivial real solutions,…
A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…