Related papers: Some exact solutions for the Caudrey-Dodd-Gibbon e…
New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorithms of power geometry are used. The method is applied for…
Exact solutions with the initial conditions are presented in the cubic duffing equation. These exact solutions are expressed in terms of the leaf function and the trigonometric function. The leaf functions: $r=sleaf_n(t) $ or $…
We have studied the solutions of the combined sine-cosine-Gordon Equation found by Wazwaz (App. Math. Comp. 177, 755 (2006)) using the variable separated ODE method. These solutions can be transformed into a new form. We have derived the…
Based on the Coulomb gauge, the accurate Klein-Gordon equation in static scalar and vector potentials was derived from Klein-Gordon equation in electromagnetic environment. The correct equation developed in this comment demonstrates that…
The Dirac-Siddharth Equation has been constructed from the Siddharth hamiltonian by quantization of the energy and momentum in Pauli algebra. We have solved this equation by using tensor product of matrices.
We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of…
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…
We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the…
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class…
In this article, we study the numerical solution of the one dimensional nonlinear sine-Gordon by using the modified cubic B-spline differential quadrature method. The scheme is a combination of a modified cubic B spline basis function and…
Klein-Gordon Equation has been solved in four dimension. The potential has been chosen to be any arbitrary field Potential.
We present various exact solutions of a discrete complex Ginzburg-Landau (CGL) equation on a plane lattice, which describe target patterns and spiral patterns and derive their stability criteria. We also obtain similar solutions to a system…
In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately…
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations,…
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
We show that the Riccati--Pad\'{e} method is suitable for the calculation of the complex eigenvalues of the Schr\"{o}dinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
The B\"acklund transformations and the superposition formulas for two sub--equations of the general elliptic equation are constructed from the Riccati equation by using an indirect mapping method.The thirty-six previously known solutions of…
In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012--4024, with respect to the convergence of the accelerated Riccati iteration method for solving the…
We derive guaranteed bounds of distance to the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet-Neumann boundary condition. It is shown that two-sided error estimates are directly computable and equivalent…