Expfunction method has been applied to solve many functional equations so far. But it hasn't been used for systems of differential-difference directly. In this paper, modified Exp-function method is introduced to obtain exact solutions of the nonlinear differential-difference systems for the first time. Furthermore, new exact solutions have been obtained for the well known Toda-Lattice system b...

Abstract: In this paper, new algorithms called the “Modified exp( ́Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp( ́Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The a...

Two novel modifications of the exp-function method have been suggested to solve nonlinear system partial differential equation fractional order for first time. The fractional-order Hirota-Satsuma coupled KdV has solved precisely; as a result, some exact solutions, which include soliton-type and rational will be derived. Eventually, graphs obtained results illustrated at end article. newly used ...

The capability of Extended tanh–coth, sine–cosine and Exp-Function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed. In this study, the generalized nonlinear Schrödinger (GNLS) equation is solved by three different methods. To obtain the single-soliton solutions for the equation, t...

The purpose of this paper is to explore the relationship between I∆0+exp and its weaker subtheories. We give a method of translating certain classes of I∆0+exp proofs into weaker systems of arithmetic such as Buss’ systems S2. We show if IEi(exp) ` A with a proof P of expindrank(P ) ≤ n + 1 where all (∀ ≤: right) or (∃ ≤: left) have bounding terms not containing function symbols then Si 2 ⊇ IEi...

This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They generalized Kudryashov method and modified exp -expansion function method. Dark, bright dark-bright soliton solutions of procured.