An application of the Exp-function method (EFM) to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for the modified KdV equation and the generalized KdV equation. The EFM was used to construct peri- odic wave and solitary wave solutions of nonlinear evolution equations (NLEEs). This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the Exp-function method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics and applied mathematics.

In this article, a simple and new algorithm is proposed, namely the modified variational iteration algorithm-I (mVIA-I), for obtaining numerical solutions to different types of fifth-order Korteweg de-Vries (KdV) equations. In order to verify the precision, accuracy and stability of the mVIA-I method, generated numerical results are compared with the Laplace decomposition method, Adomian decomposition method, Homotopy perturbation transform method and the modified Adomian decomposition method. Comparison with the mentioned methods reveals that the mVIA-I is computationally attractive, exceptionally productive and achieves better accuracy than the others.

In this paper, by applying the non-classical symmetry method, nonclassical symmetries of the Kodryashov-Sinleschikov (K-S) and modified Korteweg-de Vries-Zaharov-Kuznetsov (mKdV-ZK) equations are obtained. Apart from classical symmetries, this theory can be effective in finding a few other solutions for a system of PDEs and ODEs. Also, non-classical symmetries of a system of PDEs can be applied to reduce the number of independent variables. By adding the invariance surface condition to the assumed equations and applying the classical symmetry method for them, non-classical symmetries are calculated. Finally, some of the group invariant solutions and the similarity reduced equations associated to non-classical symmetry are obtained.

Introduction: Carney Complex is an autosomal dominant syndrome that is defined with different tumors including myxoma in different organs, endocrine tumors and lentiginosis lesions. This is the first case report of this syndrome from Iran.Case: The patient is a 27 year old girl, referred with flank pain. Physical examination revealed hirsutism, truncal obesity, hyperpigmantasion and hypertension; Cushing's syndrome was suggested and confirmed with related classic biochemical tests. She had history of cardiac myxoma during her childhood and had been operated twice.Pituitary microadenoma and right adrenal adenoma were reported on MRI and CT-scan, respectively. Initially laparascopic right adrenalectomy was done; as expected, no remission in signs of Cushing's syndrome was observed after surgery. By laparoscopic adrenalectomy of the other site, Cushing's syndrome resolved. Pathologic report of 1st operation was adrenal adenoma with surrounding pigmented micronodular hyperplasia and of the 2nd one was just pigmented micronodular hyperplasia.Conclusion: We have reported a patient with Carney syndrome along with Cushing's syndrome due to bilateral adrenal hyperplasia and an adenoma in contralateral adrenal and microadenoma of the pituitary as an incidentaloma. This is a new presentation of Carney syndrome.