Abstract
In this study, the improved tan(ϕ (ξ) /2)-expansion method (ITEM), one of the improved expansion methods, has been applied to (3+1)- dimensional Jimbo Miwa and Sharma-Tasso-Olver equations using symbolic computation. With the aid of the method, many new and abundant analytical solutions have been obtained. The newly obtained results show that ITEM is a new and significant technique for solving nonlinear differential equations which plays an important role on fluids mechanics, engineering and many physics fields.
Highlights
Scientists have used mathematics to describe the physical properties of the universe for many years by modelling
The aim of the current study is to derive new analytical solutions of (3+1)-dimensional Jimbo Miwa (JM) and Sharma-Tasso-Olver (STO) equations which are physical model by using an improved expansion method called as improved tan(φ (ξ) /2)-expansion method
The rest of the study is organized as follows, in the second section is a description of improved tan(φ (ξ) /2)-expansion method (ITEM) and third section consists of an application of the method to the STO and JM equations and newly obtained results
Summary
Scientists have used mathematics to describe the physical properties of the universe for many years by modelling. Obtain analytical and numerical solutions for differential equations is a significant part of scientific studies. The aim of the current study is to derive new analytical solutions of (3+1)-dimensional Jimbo Miwa (JM) and Sharma-Tasso-Olver (STO) equations which are physical model by using an improved expansion method called as improved tan(φ (ξ) /2)-expansion method. Of the study, we are going to present the algorithm of ITEM for constructing analytical solutions of nonlinear differential equations succesfully. Step 3: In this step, substitution of derivatives for u (ξ) respect to ξ into (3) is going to be carried out After this proceeding, a polynomial yields in term of tan (φ (ξ) /2)k and cot (φ (ξ) /2)k(k = 1, 2, ...) function. Step 4: At the final step, after solving the algebraic equation systems which are obtained in Step 3 for A0, Ak,Bk and μ and using these values in (4) with Families 1 ∼ 19 seen in Ref.[7] , the desired solutions are obtained
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