Nonlinear theory of random vibrations

TK Caughey - Advances in applied mechanics, 1971 - Elsevier
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 symmetries of differential equations: classical results and recent contributions

F Oliveri - Symmetry, 2010 - mdpi.com
Lie symmetry analysis of differential equations provides a powerful and fundamental
framework to the exploitation of systematic procedures leading to the integration by …

[图书][B] Handbook of nonlinear partial differential equations: exact solutions, methods, and problems

AD Polyanin, VF Zaitsev - 2003 - taylorfrancis.com
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 …

New similarity reductions of the Boussinesq equation

PA Clarkson, MD Kruskal - Journal of Mathematical Physics, 1989 - pubs.aip.org
Some new similarity reductions of the Boussinesq equation, which arises in several physical
applications including shallow water waves and also is of considerable mathematical …

Symmetry and separation of variables

W Miller Jr - 1977 - osti.gov
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 …

[图书][B] Lie symmetry analysis of fractional differential equations

MS Hashemi, D Baleanu - 2020 - taylorfrancis.com
The trajectory of fractional calculus has undergone several periods of intensive
development, both in pure and applied sciences. During the last few decades fractional …

Non-classical symmetry reduction: example of the Boussinesq equation

D Levi, P Winternitz - Journal of Physics A: Mathematical and …, 1989 - iopscience.iop.org
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 …

[图书][B] Методы решения нелинейных уравнений математической физики и механики

А Полянин, В Зайцев, А Журов - 2022 - books.google.com
Описаны точные аналитические методы решения нелинейных уравнений
математической физики. Наряду с классическими методами представлены также …

Symmetries and integrability

AS Fokas - Studies in Applied Mathematics, 1987 - Wiley Online Library
Integrable nonlinear evolution equations in one‐spatial and one‐temporal dimensions
possess a remarkably rich algebraic structure: Infinitely many symmetries and conserved …

Symmetry reductions and exact solutions of a class of nonlinear heat equations

PA Clarksonz, EL Mansfield - Physica D: Nonlinear Phenomena, 1994 - Elsevier
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 …