Monge-Ampère equations of the form, uxxuyy - u2
xy = F(u, ux, uy) arise in many
areas of fluid and solid mechanics. Here it is shown that in the special case F =
yf(u, ux/uy), where f denotes an arbitrary function, the Monge-Ampère equation
can be linearized by using a sequence of Ampère, point,...
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions
is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.
Considering the coupled envelope equations in nonlinear couplers, the question of integrability is attempted. It is explicitly shown that Hirota's bilinear method is one of
the simple and alternative techniques to Painlevé analysis to obtain the integrability
conditions of the coupled nonlinear Schrödinger...
In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlevé
analysis) to the classical version of the two dimensional Bukhvostov-Lipatov model.
We are led to the conclusion that the model is not integrable classically, except at a
trivial point where the theory can be described...
In this paper we give a method to obtain Darboux transformations (DTs) of integrable
equations. As an example we give a DT of the dispersive water wave equation. Using
the Miura map, we also obtain the DT of the Jaulent-Miodek equation.
Electromagnetic wave propagation through cold collision free plasma is studied using
the nonlinear perturbation method. It is found that the equations can be reduced to
the modified Kortweg-de Vries equation.
A new definition for the electromagnetic field velocity is proposed. The velocity depends on the physical fields.
The question posed by the title of this paper is, surprisingly, not yet answered uniquely
today; not even by way of definition. According to modern assumptions the light is the
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton
form. The difference between the commutator and its principal part, the Poisson
bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their...
Under the Neumann constraints, each equation of the KdV hierarchy is decomposed
into two finite dimensional systems, including the well-known Neumann model. Like in
the case of the Bargmann constraint, the explicit Lax representations are deduced from
the adjoint representation of the auxiliary spectral...
In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton
equation and (ii) (2+1)-dimensional nonlinear Schrödinger...
Switching model with one predator and two prey species is considered. The prey
species have the ability of group defence. Therefore, the predator will be attracted
towards that habitat where prey are less in number. The stability analysis is carried
out for two equilibrium values. The theoretical...