New variational principles for systems of partial differential equations

[摘要] The question of finding variational principles for coupledsystems of first order partial differential equations is considered.Using a potential representation for solutions of the first ordersystem a higher order system is obtained. Existence of a variationalprinciple follows if the original system can be transformed toa self-adjoint higher order system. Existence of variationalprinciples for all linear wave equations with constant coefficientshaving real dispersion relations is established. The method ofadjoining some of the equations of the original system to a suitableLagrangian function by the method of Lagrange multipliers is usedto construct new variational principles for a class of linear systems.The equations used as side conditions must satisfy highly-restrictiveintegrability conditions. In the more difficult nonlinear case thesystem of two equations in two independent variables can be analyzedcompletely. For systems determined by two conservation laws theside condition must be a conservation law in addition to satisfyingthe integrability conditions.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics