In this paper, we study the time variable coefficient modified Korteweg-de Vries (mKdV) equation from group-theoretic point of view. We obtain Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary variable coefficients. Finally, the solitary ...

Fourth-order combined compact finite difference scheme is given for solving the time fractional convection–diffusion–reaction equation with variable coefficients. We introduce the flux as a new variable and transform the original equation into a system of two equations. Compact difference is used as a high-order approximation for spatial derivatives of integer order in the coupled partial diffe...

We develop a High Order Fourier solver for nonseparable, selfadjoint elliptic equations with variable (diffusion) coefficients. The solution of an auxiliary constant coefficient equation, serves in a transformation of the dependent variable. There results a ”modified Helmholtz” elliptic equation with almost constant coefficients. The small deviations from constancy are treated as correction ter...

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines ...

This paper is devoted to seek new optical soliton solutions of nonlinear Schrödinger equation (NLSE) with time-dependent coefficients which describes the dispersion decreasing fiber. To achieve NLSE, basic idea homogenous balance approach has been used propose Bernoulli $$(G'/G)$$ -expansion method, where $$G =G(\zeta )$$ satisfies equation, easier solve than previous studies. By applying some ...

We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some ...