Linear and nonlinear Schrodinger equations often arise inmany branches of physics and engineering science suchas in quantum mechanics, optics and plasma physicsamong others.
The study of these equations and theirsolutions has become of great interest to manyresearchers due to its various applications. To cite a few,Wazwaz 1 utilized the Adomian decomposition methodas a reliable technique for treatment of Schrodingerequations. In Wazwaz 2, the variational iteration methodwas used to determine the exact solutions for both linearand nonlinear Schrodinger equations. Also, Zhang et al3 used the He’s frequency formulation as a method tosearch for the solutions of Schrodinger equations, and thesolutions determined turn out to be in good agreementwith the results determined in 1,2. However, we intendto couple the Elzaki transform established recently byElzaki 4 with the celebrated method of the 80th; theAdomian decomposition method 5,6.
The Elzakitransform is known for its effectiveness in solving linearordinary differential equations, linear partial differentialequation and integral equations among its competingtransforms as demonstrated in 7,8,9 While on the otherhand, the Adomian decomposition method 5,6 is awell-known method for solving linear and nonlinear,homogeneous and nonhomogeneous differential andpartial differential equations, integro-differential andfractional differential equations that gives exact solutionsin form of a convergent series. Further, the Adomiandecomposition method is also proven be to an effectiveand powerful method for treating the afore mentionedequations after the successes recorded by manyresearches such as in 10,11,12,13,14,15,16.It is expected in the end of this study that thiscoupling, the Elzaki decomposition method would giveexact solutions for the linear and nonlinear Schrodingerequations under consideration in relation to otherdecompositions methods that also work perfectly in othersettings such as in Laplace decomposition method 17,Sumudu decomposition method 18, Naturaldecomposition method 19, Aboodh decompositionmethod 20 and other couplings available in the literatureas the effectiveness of both the Elzaki transform and theAdomian decomposition method cannot beoverestimated. perspective.