Related papers: A multiple exp-function method for nonlinear diffe…
In the series of recent publications we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless…
In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schr\"odinger equations depending on two variables and of nonlinear wave equations depending on three variables.
In this paper, a variable-coefficient Boiti-Leon-Manna-Pempinelli equation is to be investigated. We obtain abundant multi-wave, breather wave and lump solutions by using the three waves method, the homoclinic breather approach and the…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
Efficient and accurate numerical simulation of seismic wave propagation is important in various Geophysical applications such as seismic full waveform inversion (FWI) problem. However, due to the large size of the physical domain and…
A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution…
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…
Real-world scenarios frequently involve multi-objective data-driven optimization problems, characterized by unknown problem coefficients and multiple conflicting objectives. Traditional two-stage methods independently apply a machine…
Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of…
In this paper a novel method to solve the constant coefficient wave equation, subject to interface jump conditions, is presented. In general, such problems pose issues for standard finite difference solvers, as the inherent discontinuity in…
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…