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We describe the new version (v2.38j) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have…

We study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by further developing the method based on the theory of viscosity solutions of…

Analysis of PDEs · Mathematics 2021-01-22 King-Yeung Lam , Xiao Yu

Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompressible, infinitely deep fluid with a free…

Classical Physics · Physics 2020-02-20 Francesco Fedele , Denys Dutykh

In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the reaction function at concentration $u=u_c$. For fixed…

Analysis of PDEs · Mathematics 2020-09-08 A. D. O. Tisbury , D. J. Needham , A. Tzella

In this article, we present a comprehensive analytical study to obtain the exact traveling wave solutions to a new formed model of the (2+1)-dimensional BKP equation. We construct exact solutions of the considered model using a recently…

Mathematical Physics · Physics 2024-01-04 Rajib Mia

The Hamiltonian formulation of the water wave problem due to Zakharov, and the reduced Zakharov equation derived therefrom, have great utility in understanding and modelling water waves. Here we set out to review the cubic Zakharov equation…

Fluid Dynamics · Physics 2026-03-12 Raphael Stuhlmeier

We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (KPP) equation with a nonlocal diffusion and an almost-periodic nonlinearity. By employing and adapting the theory of homogenization, we show that solutions of this equation…

Analysis of PDEs · Mathematics 2016-01-19 Yan Zhang

We show that the isotropic 3-wave kinetic equation is equivalent to the mean field rate equations for an aggregation-fragmentation problem with an unusual fragmentation mechanism. This analogy is used to write the theory of 3-wave…

Statistical Mechanics · Physics 2015-05-13 C. Connaughton

The $b$-family-Kadomtsev-Petviashvili equation ($b$-KP) is a two dimensional generalization of the $b$-family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with…

Analysis of PDEs · Mathematics 2024-01-17 Robin Ming Chen , Lili Fan , Xingchang Wang , Runzhang Xu

We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (KPP) equation with a nonlocal diffusion and a stationary ergodic nonlinearity. By employing and adapting the theory of stochastic homogenization, we show that solutions of…

Analysis of PDEs · Mathematics 2014-12-09 Yan Zhang

We propose and rigorously analyze a finite element method for the approximation of stationary Fokker--Planck--Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients,…

Numerical Analysis · Mathematics 2025-06-19 Timo Sprekeler , Endre Süli , Zhiwen Zhang

Deep inelastic scattering at small x can be described very effectively using saturation inspired dipole models. We investigate whether such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is…

High Energy Physics - Phenomenology · Physics 2007-06-13 Daniel Boer , Andre Utermann , Erik Wessels

In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the gravitational deflection of light in General Relativity near Schwarzschild black hole surrounded by quintessence (Kiselev…

General Relativity and Quantum Cosmology · Physics 2019-02-22 V. K. Shchigolev , D. N. Bezbatko

We investigate the stability of plane wave solutions of equations describing quantum particles interacting with a complex environment. The models take the form of PDE systems with a non local (in space or in space and time) self-consistent…

Analysis of PDEs · Mathematics 2023-10-24 Thierry Goudon , Simona Rota Nodari

The solution to the impact-parameter dependent Balitsky-Kovchegov equation with the collinearly improved kernel is studied in detail. The solution does not present the phenomenon of Coulomb tails at large impact parameters that have…

High Energy Physics - Phenomenology · Physics 2019-09-18 D. Bendova , J. Cepila , J. G. Contreras , M. Matas

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number $\kappa$ in bounded domains in $\mathbb{R}^d$. The discrete trial and test spaces are generated from…

Numerical Analysis · Mathematics 2015-10-20 Daniel Peterseim

This paper addresses biquadratic polynomial programming (BPP), an NP-hard optimization problem closely related to biquadratic tensors. We first establish several necessary and sufficient conditions for the positive semi-definiteness and…

Optimization and Control · Mathematics 2026-01-22 Haibin Chen , Yixuan Chen , Liqun Qi

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 KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(\beta-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\beta>1/3$). This equation admits ---…

Analysis of PDEs · Mathematics 2018-11-14 Mats Ehrnström , Mark Groves

In this paper, we study traveling wave solutions and peakon weak solutions of the modified Camassa-Holm (mCH) equation with dispersive term $2ku_x$ for $k\in\mathbb{R}$. We study traveling wave solutions through a Hamiltonian system…

Mathematical Physics · Physics 2017-03-23 Yu Gao , Lei Li , Jian-Guo Liu