Related papers: Solutions to the Kaup--Broer System and Its 2+1 Di…

We study the Klein-Gordon-Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the global existence of solutions and characterize their sharp…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition…

We consider certain boundary conditions supporting soliton solutions in the generalized non-linear Schr\"{o}dinger equation (AKNS$_r$)\,($r=1,2$). Using the dressing transformation (DT) method and the related tau functions we study the…

A class of negative order Ablowitz--Kaup--Newell--Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of the first order linear system of three equations. The inverse scattering problem on the whole axis are…

For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction…

We present a class of dynamical solutions for an intersecting D4-D8 brane system in ten-dimensional type IIA supergravity. The dynamical solutions reduces to a static warped AdS_6 x S^4 geometry in a certain spacetime region. We also…

``Vectorial'' numerical algorithms are proposed for solving the inverse and direct spectral scattering problems for the nonlinear vector Schroedinger equation, taking into account wave polarization, known as the Manakov system. It is shown…

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg--de Vries, equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave…

We present a novel numerical framework for studying nonlinear dispersive equations in higher-dimensional settings, specifically designed for solutions featuring traveling waves along a preferred axis (or field-aligned traveling waves).…

Although the Kadanoff-Baym equations are typically solved using time-stepping methods, iterative global-in-time solvers offer potential algorithmic advantages, particularly when combined with compressed representations of two-time objects.…

The Whitham Broer Kaup (WBK) equations provide a fundamental framework for modeling shallow water wave dynamics, effectively capturing both nonlinear and dispersive effects. In this study, we construct a new class of analytical and…

Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we…

We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\"odinger equation with an…

We combine the observable-based formalism (KMOC), the analytic properties of the scattering amplitude, generalised unitarity and the heavy-mass expansion with a newly introduced IBP reduction for Fourier integrals, to provide an efficient…

A dressing scheme applicable to Dunajski equation is developed. Simple example of constructing solutions in terms of implicit functions is considered. Dunajski equation hierarchy is described, its Lax-Sato form is presented. Dunajsky…

We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr\"odinger equation. We prove that a particular class of integrators are conjugate to unitary methods for…

In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…

In the present work we give a generalization of the hyperboloidal foliation method which allows us to remove the restriction on support of initial data in $\mathbb{R}^{1+1}$. Then we will make an application on a model system.