Related papers: Conservation laws for a $q$-deformed nonrelativist…
For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating…
We consider time-dependent Schr\"{o}dinger equations for a free nonrelativistic particle on the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to these Schr\"{o}dinger equations and show that they form a…
We introduce $q$-versions of the Klein-Gordon equation in the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to our $q$-deformed Klein-Gordon equations. We show that these plane wave solutions form a…
We construct a new nonlinear deformed Schr\"odinger structure using a nonlinear derivative operator which depends on a parameter $q$. This operator recovers Newton derivative when $q \rightarrow 1$. Using this operator we propose a deformed…
For nonlinear Schr\"odinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…
We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schr\"odeinger fields, assuming that an initial density operator takes a special form of the local Gibbs…
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…