Related papers: Evolution equations: Frobenius integrability, cons…
We consider evolution equations describing the scale dependence of the wave function of a baryon containing an infinitely heavy quark and a pair of light quarks at small transverse separations, which is the QCD analogue of the helium…
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing,…
In the present paper the smoothness loss of a continuation of solutions to convolution equations is studied. Also examples for some kinds of convolvers are given.
We couple the issue of evolution in the laws of physics with that of violations of energy conservation. We define evolution in terms of time variables canonically dual to ``constants'' (such as $\Lambda$, the Planck mass or the…
The aim of this paper is to prove stability of traveling waves for integro-differential equations connected with branching Markov processes. In other words, the limiting law of the left-most particle of a (time-continuous) branching Markov…
We continue the development of $\mathbb{Z}^n_2$-supergeometry, a natural generalization of classical ($\mathbb{Z}_2$-graded) supergeometry, by proving the Frobenius theorem for integrable distributions on differentiable…
It is well-known that by requiring solutions of the Camassa--Holm equation to satisfy a particular local conservation law for the energy in the weak sense, one obtains what is known as conservative solutions. As conservative solutions…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
The Liouville-von Neumann equation describes the change in the density matrix with time. Interestingly, this equation was recently regarded as a wave equation for wave functions but not a equation for density functions. This setting leads…
We investigate the integrability of Fr\'{e}chet tangent distributions on Fr\'{e}chet manifolds. We introduce the local well-posedness Condition W for split tangent subbundles, which reduces the local integrability problem to solving initial…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
In this paper, we complement recent results of Bronski and Johnson and of Johnson and Zumbrun concerning the modulational stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation. In this…
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…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of which generates the original traveling waves, and the other…
We show that, for certain evolution partial differential equations, the solution on a finite interval $(0,\ell)$ can be reconstructed as a superposition of restrictions to $(0,\ell)$ of solutions to two associated partial differential…
In this article, a modification of the rapidly convergent approximation method is proposed to solve a coupled Korteweg-de Vries equations with conformable derivative that govern shallow-water waves. Based on the Leibniz and chain rule of…
We consider space-periodic evolutionary and travelling-wave solutions to the regularised long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial…
Surface waves in a heated viscous fluid exhibit a long wave oscillatory instability. The nonlinear evolution of unidirectional waves is known to be described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the present work…
We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…