Analytical exact solutions for the Razavy type potential

Karayer, H.; Demirhan, D.; Atman, Kazım Gökhan

doi:10.1002/mma.6612

Cited by 7 publications

(3 citation statements)

References 22 publications

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“…up to arbitrary m into the n-term truncated residual functions (49) to get the required components for expansion (48) as in the following procedure: for first approximations ( ) ( )…”

Section: One-dimensional Nonlinear Coupled Time-fmtesmentioning

confidence: 99%

“…Further, a fractional differential equation is said to be causal if it involves fractional derivatives of a single type. In physics, the left fractional derivative according to the time domain represents the previous state of the dynamical process, while the right fractional derivative indicates the future one [47,48]. In the application of quantum mechanics, the right fractional derivatives can be used to describe the velocity of an antiparticle due to Feynman's and Stückelberg's views about 'antiparticles propagate backward in time'.…”

Section: Introductionmentioning

confidence: 99%

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Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method

2020

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In quantum field theory, the fractional Kundu-Eckhaus and massive Thirring models are nonlinear partial differential equations under fractional sense inside nonlinear Schrödinger class. In this study, approximate analytical solutions of such complex nonlinear fractional models are acquired by means of conformable residual power series method. This method presents a systematic procedure for constructing a set of periodic wave series solutions based on the generalization of conformable power series and gives the unknown coefficients in a simple pattern. By plotting the solutions behavior of the models; the convergence regions in which the solutions coincide to each other are checked for various fractional values. The approximate solutions generated by the proposed approach are compared with the exact solutions -if exist- and the approximate solutions obtained using qHATM and LADM. Numerical results show that the proposed method is easy to implement and very computationally attractive in solving several complex nonlinear fractional systems that occur in applied physics under a compatible fractional sense.

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“…up to arbitrary m into the n-term truncated residual functions (49) to get the required components for expansion (48) as in the following procedure: for first approximations ( ) ( )…”

Section: One-dimensional Nonlinear Coupled Time-fmtesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method

2020

View full text Add to dashboard Cite

show abstract

“…On the other hand, in 1980 M. Razavy used double potential wells in the quantum theory of molecules to describe the motion of a particle in the presence of two force fields [45]. These types of potentials are known today as Razavy potentials [46,47], and are used as a model to describe the coupling of two molecules or quantum dots [48][49][50][51]. Effects of intense laser field and position dependent effective mass in Razavy QWs (Razavy-like quantum wells) were investigated in Ref.…”

Section: Introductionmentioning

confidence: 99%