Publisher Summary Random vibration analysis of mechanical systems has become an
important subject in recent years, principally because of advances in high speed flight. To …

Lie symmetry analysis of differential equations provides a powerful and fundamental
framework to the exploitation of systematic procedures leading to the integration by …

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

Some new similarity reductions of the Boussinesq equation, which arises in several physical
applications including shallow water waves and also is of considerable mathematical …

This book is concerned with the relation between symmetries of a linear second-order partial
differential equation of mathematical physics, the coordinate systems in which the equation …

The trajectory of fractional calculus has undergone several periods of intensive
development, both in pure and applied sciences. During the last few decades fractional …

A symmetry of an equation will leave the set of all solutions invariant. A'conditional
symmetry'will leave only a subset of solutions, defined by some differential condition …

Описаны точные аналитические методы решения нелинейных уравнений
математической физики. Наряду с классическими методами представлены также …

Integrable nonlinear evolution equations in one‐spatial and one‐temporal dimensions
possess a remarkably rich algebraic structure: Infinitely many symmetries and conserved …

Classical and nonclassical symmetries of the nonlinear heat equation ut= u xx+ f (u) are
considered. The method of differential Gröbner bases is used both to find the conditions on f …