We study the class of generalized Korteweg–de Vries (KdV) equations derivable from the
Lagrangian: L (l, p)= F [1/2 cphi x cphi t-(cphi x) l/l (l-1)+ α (cphi x) p (cphi xx) 2] dx, where the …

We study the class of shallow water equations of Camassa and Hold derived from the
Lagrangian, L=∫[1 2 (ϕ xxxx− ϕ x) ϕ t− 1 2 (ϕ x) 3− 1 2 ϕ x (ϕ xx) 2− 1 2 κ ϕ x 2] dx, using a …

Solitons play a fundamental role in the evolution of general initial data for quasilinear
dispersive partial differential equations, such as the Korteweg–de Vries (KdV), nonlinear …

In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as
systems of coupled stochastic and partial differential equations, and we derive stochastic …

It is well known that the Korteweg–de Vries (KdV) equation has an infinite set of conserved
quantities. The first three are often considered to represent mass, momentum, and energy …

In this paper, we constructed the variational principles for Bogoyavlensky–Konopelchenko
equation, the generalized (3+ 1)-dimensional nonlinear wave in liquid containing gas …

In this paper, we formulate the least action principle for organized system as the minimum of
the total sum of the actions of all of the elements. This allows us to see how this most basic …

This book provides an up-to-date (2018) presentation of the shallow water problem
according to a theory which goes beyond the Korteweg-de Vries equation. When we began …

We derive a new variational principle, leading to a new momentum map and a new
multisymplectic formulation for a family of Euler–Poincaré equations defined on the Virasoro …

This paper considers the P T-symmetric extensions of the equations examined by Cooper,
Shepard and Sodano. From the scaling properties of the P T-symmetric equations a general …