The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

The generalized derivative higher order non-linear Schrödinger (DNLS) equation describes
pluses propagation in optical fibers and can be regarded as a special case of the …

The derivative nonlinear Schrödinger (DNLS) equation is a nonlinear dispersive model that
appears in the description of wave propagation in a plasma. The existence of a Lagrangian …

Mechanics is a branch of physics studying motion. The history of mechanics, as well as the
history of other branches of science, is a history of attempts to explain the world by means of …

This book gives an exposition of the fundamentals of finite element theory with application to
fluid dynamics problems. The theory includes a discussion of variational principles and …

The fundamental importance of functional differential equations has been recognized in
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …

The Korteweg–de Vries (KdV) equation with higher order nonlinearity models the wave
propagation in one-dimensional nonlinear lattice. A higher-order extension of the familiar …

In [4], Tonti gave necessary and sufficient conditions for certain differential expressions
(namely those expressions which we call" source equations"; for the definition see below or …

Deals with the general problem of finding a multiplier matrix that can give to a prescribed
system of second-order ordinary equations the structure of Euler-Lagrange equations. The …

1. Introduction. In studying physical phenomena one frequently encounters differential
equations which arise from a variational principle, ie the equations are the Euler-Lagrange …