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We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the…

High Energy Physics - Phenomenology · Physics 2008-11-26 R. Peschanski , S. Sapeta

In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a…

Analysis of PDEs · Mathematics 2025-06-03 Elena Demattè , Juan J. L. Velázquez

We analyse a generalised Fokker-Planck equation by making essential use of its linearisability through a Cole-Hopf transformation. We determine solutions of travelling wave and multi-kink type by resorting to a geometric construction in the…

Mathematical Physics · Physics 2025-04-29 Francesco Giglio , Giulio Landolfi , Luigi Martina , Andrea Zingarofalo

The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…

Optics · Physics 2019-03-27 Ulrich Brosa

The objective of this paper is to construct geometrically Riemann $k$-wave solutions of the general form of first-order quasilinear hyperbolic systems of partial differential equations. To this end, we adapt and combine elements of two…

Analysis of PDEs · Mathematics 2025-11-18 A. M. Grundland , J. de Lucas

This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high-dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the…

Analysis of PDEs · Mathematics 2024-04-08 Amin Esfahani

In this work, we apply the factorization technique to the Benjamin-Bona-Mahony like equations, B(m,n), in order to get travelling wave solutions. We will focus on some special cases for which m is not equal to n, and we will obtain these…

Exactly Solvable and Integrable Systems · Physics 2008-11-06 S. Kuru

A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both…

Mathematical Physics · Physics 2013-03-08 Julio Garralón , Francisco Rus , Francisco R. Villatoro

In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: $ u_{tt}-Lu_{xx}=B(\pm |u|^{p-1}u)_{xx}$, $ p>1$. The main characteristic of this class of…

Analysis of PDEs · Mathematics 2015-01-20 H. A. Erbay , S. Erbay , A. Erkip

The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…

Analysis of PDEs · Mathematics 2016-02-19 Alessandro Audrito , Juan Luis Vázquez

We investigate the existence and nonexistence of traveling wave solutions near monotonic shear flows with non-constant background density for the two-dimensional inhomogeneous Euler equations in a finite channel. For any small $\tau>0$,…

Analysis of PDEs · Mathematics 2026-02-03 Qi Zhao , Weiren Zhao

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…

Pattern Formation and Solitons · Physics 2015-06-26 Robert L. Pego , Jose Raul Quintero

We solve for waves in an isothermal, stratified medium with a magnetic field that points along a direction perpendicular to that of gravity and varies exponentially in the direction of gravity. We find exact analytical solutions for two…

Solar and Stellar Astrophysics · Physics 2022-06-17 B. Tripathi , Dhrubaditya Mitra

The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained.…

Exactly Solvable and Integrable Systems · Physics 2012-07-31 Nikolay K. Vitanov , Zlatinka I. Dimitrova , Holger Kantz

We consider the non-monotone degenerate diffusion equation with time delay. Different from the linear diffusion equation, the degenerate equation allows for semi-compactly supported traveling waves. In particular, we discover…

Analysis of PDEs · Mathematics 2020-06-24 Tianyuan Xu , Shanming Ji , Ming Mei , Jingxue Yin

We review the theory of modulation equations or Whitham equations for the travelling wave solution of KdV. We then apply the Whitham modulation equations to describe the long-time asymptotics and small dispersion asymptotics of the KdV…

Mathematical Physics · Physics 2018-10-10 Tamara Grava

We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…

Mathematical Physics · Physics 2018-09-18 Lang Xia

In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schr\"{o}dinger equation and of a Wick-type stochastic fractional Regularized Long Wave-Burgers (RLW-Burgers) equation have been obtained by using an…

Analysis of PDEs · Mathematics 2020-02-18 Hyunsoo Kim , Rathinasamy Sakthivel , Amar Debbouche , Delfim F. M. Torres

We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…

Analysis of PDEs · Mathematics 2025-08-19 Benjamin F. Akers , David M. Ambrose , Davia W. Sulon

We investigate thin-slit diffraction problems for two-dimensional lattice waves. The peculiar structure allows us to consider the problems on the semi-infinite triangular lattice, consequently, we study Dirichlet problems for the…

Mathematical Physics · Physics 2022-07-12 David Kapanadze , Ekaterina Pesetskaya