Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their complete integrability. The Gardner equation is chosen as the key example for it comprises both the Korteweg-de Vries and modified Korteweg de Vries (mKdV) equations. The Gardner and Miura transformations which connect these equations are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case) whereas the focusing Gardner equation has the standard elastically colliding solitons. The paper’s aim is to provide a review of integrability properties and solutions of the Gardner equation and illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica but can be adapted for major computer algebra systems.

The bonds of England and the UAE date back to over 220 years ago. This article explores the interference of Arabic prepositions in the English used in the United Arab Emirates (UAE), and their occurrences in light of gender and level of education, two important social variables related to linguistic behavior. To do so, participants will translate 20 sentences in Arabic into English as well as fill in 30 gaps in sentences in English with the missing prepositions. We will also experiment how musical intelligence may improve Emiratis’ performance regarding preposition. A study will be carried out to verify if participants from the experimental group, who will receive training on prepositions through music, obtains better results compared to the control group, who will receive training through a more traditional way (by listening to the instructor and repeating).

The concept of spiritual intelligence is currently at the focus of scientific debate. One of the most important problems is if it is a valid intelligence that meets the criteria developed by scholars. In this paper, I look at this idea in the context of Howard Gardner's theory of multiple intelligences and show some evidence from biology, neurology, and other scientific disciplines