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A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.
Spectral lines of helium are commonly observed on the Sun. These observations contain important informations about physical conditions and He/H abundance variations within solar outer structures. The modeling of chromospheric and coronal…
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to viscosity solutions. We begin by describing a fundamental…
We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We give the explicit form of one- and two- solitonic solutions and study them in detail. We distinguish a special…
Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
We establish dispersion engineering rules that allow us to control the thermalization process and the thermal state of an initial beam propagating in a multimode nonlinear photonic circuit. To this end, we have implemented a kinetic…
When modelling phase change, the latent heat released (absorbed) during solidification (melting) must be included in the heat transfer equation. In this paper, different SPH methods for the implementation of latent heat, in the context of…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when the underlying temperature is not constant. The aim of this…
This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of linear PDEs which expresses solutions using sums of polynomials…
We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled…
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides…
We consider the steady heat transfer between a collection of impermeable obstacles immersed in an incompressible 2D potential flow, when each obstacle has a prescribed boundary temperature distribution. Inside the fluid, the temperature…
Asymptotic methods are used to derive a geometrically nonlinear beam model for thermoelastic solids with a spatially localised heat source. The asymptotic reduction is based on collapsing the heated region to a point. Away from the point of…
Boiling is a complex phenomenon where different non-linear physical interactions take place and for which the quantitative modeling of the mechanism involved is not fully developed yet. In the last years, many works have been published…
In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic…
The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest…
In this paper, diffusion in polymer solutions undergoing evaporation of solvent is modeled as a coupled heat and mass transfer problem with moving boundary condition within the framework of nonequilibrium thermodynamics. The proposed…