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This study presents new soliton solutions for the nonlinear fractional twin-core couplers with Kerr law nonlinearity by employing the modifed extended tanh method with Riccati equation. The solutions are expressed in terms of some elementary functions including rational, trigonometric and hyperbolic types. Graphical demonstrations of the simulations are provided.

A new local fractional-order derivative operator is introduced and the Lakshmanan–Porsezian–Daniel (LPD) model is interpreted via this operator. New analytical solutions to the LPD equation is presented by Jacobi elliptic functions and an anzätz method. The complex-valued LPD equation includes a nonlinear term which is considered from three diferent cases: Kerr, parabolic and anti-cubic law of nonlinearities. For each case, dark, bright, singular optical soliton solutions related with optical fbers are presented. Simulations representing behavior of these solutions for diferent parameter values are provided.

We are concerned with new form optical solitons to the non-linear Schrodinger equation (NLSE) by generalized anti-cubic non-linearity. Some new optical solitons containing dark, singular and periodic solitons in chirp-free and chirped form are constructed via modified extended tanh expansion method. These results are very useful in the field of optics. The obtained results are verified and also explain by drawing different graphs. Parametric conditions for the chirp-free and chirped shape soliton solutions are also mentioned. Computational results indicate the efficiency of the aforesaid analytical expansion scheme.

In this paper, we present a new method for integration of 3-D medical data by utilizing the advantages of 3-D multiresolution analysis and techniques of variational calculus. We first express the data integration problem as a variational optimal control problem where we express the displacement field in terms of wavelet expansions and, secondly, we write the components of the displacement field in terms of wavelet coefficients. We solve this optimization problem with a blockwise descent algorithm. We demonstrate the registration of 3-D brain MR images in the size of 257 × 257 × 65 as an application of the present method. Experimental results indicate that the method can integrate 3-D MR images better than only variational or only wavelet-based methods. MSC: 68U10, 65D18, 65J05, 97N40.