Mathematics for Physics: The implicit bogning functions & applications

Our research work in recent years has focused on the propagation of solitary waves in some transmission media such as optical fiber, power lines, atomic chains, crystalline, ... in short in nonlinear media in general. During these studies, the difficulty of constructing such types of solutions, sometimes forced into different transmission media allowed to find a function having an explicit and implicit form, which has the merit of grouping hyperbolic functions within it, trigonometric and exponential. This function with very interesting properties allowed to better build the solutions of certain types of nonlinear partial differential equations. It presents simple forms that boil down to classic hyperbolic and trigonometric functions. With this in mind, I felt it urgent to make available to the public a book to prepare undergraduate students to better understand the contours of the above function which is at the center of many problems of nonlinear physics and mathematics. This pioneering book is the result of 10 years of research and includes 13 chapters that review the simple implicit functions of Bogning in all its forms. Using these, many problems of physics are also treated.