Handbook of exact solutions to mathematical equations algebraic equations, integral equations, functional equations, differential equations

"This Handbook is a unique reference for scientists and engineers, containing over 3,800 nonlinear partial differential equations with solutions. The book concerns first-, second-, third-, fourth-, and higher-order nonlinear PDEs and systems of coupled PDEs. It discusses parabolic, hyperbolic, and elliptic equations as well as those of mixed and general type. All in all, the handbook contains many more nonlinear equations of mathematical physics and other nonlinear PDEs with their exact solutions, than any other book currently available. Apart from the exact solutions, it also provides various reductions and transformations leading to ordinary differential equations, linear PDEs, or simpler PDEs. A solution is called exact if, when substituted into the differential equation under consideration, it turns the equation into an identity. In this case, no approximations or simplifications of the equation are allowed, and no a priori assumptions are used. Exact solutions to nonlinear equations of mathematical physics are understood as follows: solutions expressed in terms of elementary functions, functions included in the equation (this is necessary when the equation depends on arbitrary functions), and indefinite integrals; solutions expressed in terms of solutions to ordinary differential equations or systems of such equations. Exact solutions of mathematical equations have always played and continue to play a massive role in forming a correct understanding of the qualitative features of many phenomena and processes in various fields of natural science. The book will be helpful for a wide range of researchers, university teachers, and graduate and postgraduate students specializing in the fields of applied and computational mathematics, mathematical and theoretical physics, continuum mechanics, control theory, biology, biophysics, biochemistry, medicine, chemical engineering sciences, and ecology"--